Mathematics · Textbook solutions

Some Applications of Trigonometry

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 22 questions

9.1 Heights and Distances

22 q

Solved Examples

Worked · 7

9.1 Eg.1 $60^\circ$
9.1 Eg.2 $60^\circ$
9.1 Eg.3 $45^\circ$
9.1 Eg.4 $30^\circ$
9.1 Eg.5 $30^\circ$
9.1 Eg.6 $30^\circ$
9.1 Eg.7 $30^\circ$

Exercise 9.1

Practice · 15

Ex 9.1 Q1 $30^\circ$
Ex 9.1 Q2 $30^\circ$
Ex 9.1 Q3 $30^\circ$
Ex 9.1 Q4 $30^\circ$
Ex 9.1 Q5 $60^\circ$
Ex 9.1 Q6 $30^\circ$
Ex 9.1 Q7 $45^\circ$
Ex 9.1 Q8 $60^\circ$
Ex 9.1 Q9 $30^\circ$
Ex 9.1 Q10 $60^\circ$
Ex 9.1 Q11 $60^\circ$
Ex 9.1 Q12 $60^\circ$
Ex 9.1 Q13 $30^\circ$
Ex 9.1 Q14 $60^\circ$
Ex 9.1 Q15 $30^\circ$

What the board has asked from this chapter

Questions per paper · 67 papers · 2022 to 2026

2026

22 q

9 $30^\circ$
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Angle of Elevation Problems
9 $\sqrt{3}$
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Angle of Elevation Problems
11 $10\sqrt{3}$
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Angle of Elevation Problems
12 $45^\circ$
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Angle of Elevation Problems
17 $60^\circ$
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Angle of Elevation Problems
32 $60^\circ$
Angle of Elevation Problems
34 (a) $30^\circ$
Angle of Elevation Problems
34 $30^\circ$
Angle of Elevation Problems
34 (b) $30^\circ$
Angle of Depression Problems
35 $30^\circ$
Angle of Elevation Problems
Tejas is standing at the top of a building and observes a car at an angle of depression of $30^\circ$ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to $60^\circ$ , and at that moment, the car is 25 m away from the building. Based on the information given above, answer the following questions :
37 (i) $What is the height of the building ?$
Angle of Depression Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’ (as shown in figure). Distance between the base of the tower and point ‘O’ is 6 m. From point ‘O’, the angle of elevation of the top of the section ‘B’ is $30^\circ$ and the angle of elevation of the top of section ‘A’ is $60^\circ$ . Based on the above information, answer the following questions :
37 (i) $Find the length of the wire from the point ‘O’ to the top of section ‘B’.$
Angle of Elevation Problems
Tejas is standing at the top of a building and observes a car at an angle of depression of $30^\circ$ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to $60^\circ$ , and at that moment, the car is 25 m away from the building. Based on the information given above, answer the following questions :
37 (ii) $What is the distance between the two positions of the car ?$
Angle of Depression Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’ (as shown in figure). Distance between the base of the tower and point ‘O’ is 6 m. From point ‘O’, the angle of elevation of the top of the section ‘B’ is $30^\circ$ and the angle of elevation of the top of section ‘A’ is $60^\circ$ . Based on the above information, answer the following questions :
37 (ii) $Find the length of the wire from the point ‘O’ to the top of section ‘A’.$
Angle of Elevation Problems
Tejas is standing at the top of a building and observes a car at an angle of depression of $30^\circ$ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to $60^\circ$ , and at that moment, the car is 25 m away from the building. Based on the information given above, answer the following questions :
37 (iii) (a) $What would be the total time taken by the car to reach the foot of the building from the starting point ?$
Angle of Depression Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’ (as shown in figure). Distance between the base of the tower and point ‘O’ is 6 m. From point ‘O’, the angle of elevation of the top of the section ‘B’ is $30^\circ$ and the angle of elevation of the top of section ‘A’ is $60^\circ$ . Based on the above information, answer the following questions :
37 (iii) (a) $Find the distance AB.$
Angle of Elevation Problems
Tejas is standing at the top of a building and observes a car at an angle of depression of $30^\circ$ as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to $60^\circ$ , and at that moment, the car is 25 m away from the building. Based on the information given above, answer the following questions :
37 (iii) (b) $60^\circ$
Angle of Depression Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’ (as shown in figure). Distance between the base of the tower and point ‘O’ is 6 m. From point ‘O’, the angle of elevation of the top of the section ‘B’ is $30^\circ$ and the angle of elevation of the top of section ‘A’ is $60^\circ$ . Based on the above information, answer the following questions :
37 (iii) (b) $\Delta OPB$
Angle of Elevation Problems
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank. From a window (W) of the building, the angle of elevation of top of the tank is $45^\circ$ and angle of depression of its foot is $30^\circ$ .
38 (i) $Write a relation between d (the height of window) and y.$
Angle of Depression Problems
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank. From a window (W) of the building, the angle of elevation of top of the tank is $45^\circ$ and angle of depression of its foot is $30^\circ$ .
38 (ii) $Determine the value of h.$
Angle of Elevation Problems
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank. From a window (W) of the building, the angle of elevation of top of the tank is $45^\circ$ and angle of depression of its foot is $30^\circ$ .
38 (iii) (a) $Determine height of the water tank.$
Angle of Elevation Problems
Elevated water storage tanks are built to store and supply water to nearby colonies. In the diagram given above, AB is an elevated water tank and CD is a nearby multistorey building. The building is 54 metres away from the water tank. From a window (W) of the building, the angle of elevation of top of the tank is $45^\circ$ and angle of depression of its foot is $30^\circ$ .
38 (iii) (b) $x$
Angle of Elevation Problems

2025

30 q

10 $60^\circ$
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Angle of Elevation Problems
13 $10\sqrt{3}$
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Angle of Depression Problems
13 $45^\circ$
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Angle of Elevation Problems
15 $A ladder 14 m long leans against a wall. If the foot of the ladder is 7 m from the wall, then the angle of elevation of the top of the wall is :$
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Angle of Elevation Problems
17 $30^\circ$
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Angle of Elevation Problems
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
19 $60^\circ$
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Angle of Elevation Problems
32 (a) $60^\circ$
Angle of Depression Problems
32 (b) $30^\circ$
Angle of Depression Problems
35 (a) $45^\circ$
Angle of Elevation Problems
35 (b) $1{\cdot}5$
Angle of Elevation Problems
A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be $30^\circ$ and $45^\circ$ as it moves from point P to point Q. The height of the lighthouse is 50 metres. Based on the information given above, answer the following questions :
37 (i) $45^\circ$
Angle of Depression Problems
A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be $30^\circ$ and $45^\circ$ as it moves from point P to point Q. The height of the lighthouse is 50 metres. Based on the information given above, answer the following questions :
37 (ii) $\angle PBA$
Angle of Depression Problems
A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be $30^\circ$ and $45^\circ$ as it moves from point P to point Q. The height of the lighthouse is 50 metres. Based on the information given above, answer the following questions :
37 (iii) (a) $Find the distance travelled by the ship between points P and Q.$
Angle of Depression Problems
A lighthouse stands tall on a cliff by the sea, watching over ships that pass by. One day a ship is seen approaching the shore and from the top of the lighthouse, the angles of depression of the ship are observed to be $30^\circ$ and $45^\circ$ as it moves from point P to point Q. The height of the lighthouse is 50 metres. Based on the information given above, answer the following questions :
37 (iii) (b) $If the ship continues moving towards the shore and takes 10 minutes to travel from Q to A, calculate the speed of the ship in km/h, from Q to A.$
Angle of Depression Problems
Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be $60^\circ$ . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be $45^\circ$ . Based on the above given information, answer the following questions :
38 (i) $If CD is h metres, find the distance BD in terms of ‘h’.$
Angle of Elevation Problems
A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be $30^\circ$ at a particular instant. Based on above information, answer the following questions :
38 (i) $Represent the above situation with the help of a diagram.$
Angle of Depression Problems
The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation – I : The angle of elevation of the top of Statue from Place A which is $80\sqrt{3}$ m away from the base of the Statue is found to be $60^\circ$ . Situation – II : The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be $30^\circ$ and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions :
38 (i) $Represent the Situation - I with the help of a diagram.$
Angle of Elevation Problems
Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile means to travel between the aircraft doors and the ground. Larger aircraft have door sills 5 to 20 feet (1 foot = 30 cm) high. Stairs facilitate safe boarding and de-boarding. An aircraft has a door sill at a height of 15 feet above the ground. A stair car is placed at a horizontal distance of 15 feet from the plane. Based on given information, answer the questions given in part (i) and (ii).
38 (i) $Find the angle at which stairs are inclined to reach the door sill 15 feet high above the ground.$
Angle of Elevation Problems
A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be $30^\circ$ at a particular instant. Based on above information, answer the following questions :
38 (ii) $\sqrt{3} = 1.73$
Angle of Depression Problems
The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation – I : The angle of elevation of the top of Statue from Place A which is $80\sqrt{3}$ m away from the base of the Statue is found to be $60^\circ$ . Situation – II : The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be $30^\circ$ and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions :
38 (ii) $Represent the Situation - II with the help of a diagram.$
Angle of Elevation Problems
Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile means to travel between the aircraft doors and the ground. Larger aircraft have door sills 5 to 20 feet (1 foot = 30 cm) high. Stairs facilitate safe boarding and de-boarding. An aircraft has a door sill at a height of 15 feet above the ground. A stair car is placed at a horizontal distance of 15 feet from the plane. Based on given information, answer the questions given in part (i) and (ii).
38 (ii) $Find the length of stairs used to reach the door sill.$
Angle of Elevation Problems
Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be $60^\circ$ . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be $45^\circ$ . Based on the above given information, answer the following questions :
38 (ii) $Find distance BC in terms of ‘h’.$
Angle of Elevation Problems
The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation – I : The angle of elevation of the top of Statue from Place A which is $80\sqrt{3}$ m away from the base of the Statue is found to be $60^\circ$ . Situation – II : The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be $30^\circ$ and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions :
38 (iii) (a) $Calculate the height of Statue excluding the base and also find the height including the base with the help of Situation - I.$
Angle of Elevation Problems
Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile means to travel between the aircraft doors and the ground. Larger aircraft have door sills 5 to 20 feet (1 foot = 30 cm) high. Stairs facilitate safe boarding and de-boarding. An aircraft has a door sill at a height of 15 feet above the ground. A stair car is placed at a horizontal distance of 15 feet from the plane. Based on given information, answer the questions given in part (i) and (ii).
38 (iii) (a) $60^\circ$
Angle of Elevation Problems
Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be $60^\circ$ . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be $45^\circ$ . Based on the above given information, answer the following questions :
38 (iii) (a) $\sqrt{3} = 1{\cdot}73$
Angle of Elevation Problems
A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be $30^\circ$ at a particular instant. Based on above information, answer the following questions :
38 (iii) (a) $30^\circ$
Angle of Depression Problems
Amrita stood near the base of a lighthouse, gazing up at its towering height. She measured the angle of elevation to the top and found it to be $60^\circ$ . Then, she climbed a nearby observation deck, 40 metres higher than her original position and noticed the angle of elevation to the top of lighthouse to be $45^\circ$ . Based on the above given information, answer the following questions :
38 (iii) (b) $Find distance AE, if AC = 100 m.$
Angle of Elevation Problems
The Statue of Unity situated in Gujarat is the world’s largest Statue which stands over a 58 m high base. As part of the project, a student constructed an inclinometer and wishes to find the height of Statue of Unity using it. He noted following observations from two places : Situation – I : The angle of elevation of the top of Statue from Place A which is $80\sqrt{3}$ m away from the base of the Statue is found to be $60^\circ$ . Situation – II : The angle of elevation of the top of Statue from a Place B which is 40 m above the ground is found to be $30^\circ$ and entire height of the Statue including the base is found to be 240 m. Based on given information, answer the following questions :
38 (iii) (b) $\tan\alpha$
Angle of Elevation Problems
Passenger boarding stairs, sometimes referred to as boarding ramps, stair cars or aircraft steps, provide a mobile means to travel between the aircraft doors and the ground. Larger aircraft have door sills 5 to 20 feet (1 foot = 30 cm) high. Stairs facilitate safe boarding and de-boarding. An aircraft has a door sill at a height of 15 feet above the ground. A stair car is placed at a horizontal distance of 15 feet from the plane. Based on given information, answer the questions given in part (i) and (ii).
38 (iii) (b) $30^\circ$
Angle of Elevation Problems
A drone was used to facilitate movement of an ambulance on the straight highway to a point P on the ground where there was an accident. The ambulance was travelling at the speed of 60 km/h. The drone stopped at a point Q, 100 m vertically above the point P. The angle of depression of the ambulance was found to be $30^\circ$ at a particular instant. Based on above information, answer the following questions :
38 (iii) (b) $60^\circ$
Angle of Depression Problems

2024

17 q

7 $60^\circ$
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Angle of Elevation Problems
10 $\sqrt{3}$
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Angle of Elevation Problems
14 $At some time of the day, the length of the shadow of a tower is equal to its height. Then, the Sun’s altitude at that time is :$
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Angle of Elevation Problems
17 $1 : \sqrt{3}$
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Angle of Elevation Problems
32 $60^\circ$
Angle of Elevation Problems
32 $60^\circ$
Angle of Elevation Problems
32 $60^\circ$
Angle of Elevation Problems
32 $30^\circ$
Angle of Elevation Problems
32 $30^\circ$
Angle of Depression Problems
33 $30^\circ$
Angle of Depression Problems
33 $30^\circ$
Angle of Depression Problems
34 $30^\circ$
Angle of Depression Problems
34 $30^\circ$
Angle of Elevation Problems
35 $45^\circ$
Angle of Depression Problems
35 $60^\circ$
Angle of Elevation Problems
35 $30^\circ$
Angle of Depression Problems
35 $60^\circ$
Angle of Elevation Problems

2023

21 q

9 $2\sqrt{3}$
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Angle of Elevation Problems
23 $\theta$
Angle of Elevation Problems
24 (a) $\sqrt{3}$
Angle of Elevation Problems
24 (b) $30^\circ$
Angle of Elevation Problems
32 $60^\circ$
Angle of Elevation Problems
32 $45^\circ$
Angle of Elevation Problems
32 (A) $30^\circ$
Angle of Depression Problems
32 (B) $60^\circ$
Angle of Elevation Problems
33 (a) $30^\circ$
Angle of Depression Problems
33 (a) $60^\circ$
Angle of Elevation Problems
33 (b) $30^\circ$
Angle of Elevation Problems
33 (b) $60^\circ$
Angle of Elevation Problems
34 $60^\circ$
Angle of Elevation Problems
35 (a) $60^\circ$
Angle of Elevation Problems
35 $60^\circ$
Angle of Elevation Problems
35 $60^\circ$
Angle of Elevation Problems
35 (b) $30^\circ$
Angle of Depression Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of the Section B is $30^\circ$ and the angle of elevation of the top of Section A is $45^\circ$ . Based on the above information, answer the following questions :
37 (i) $Find the length of the wire from the point O to the top of Section B.$
Angle of Elevation Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of the Section B is $30^\circ$ and the angle of elevation of the top of Section A is $45^\circ$ . Based on the above information, answer the following questions :
37 (ii) (a) $Find the distance AB.$
Angle of Elevation Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of the Section B is $30^\circ$ and the angle of elevation of the top of Section A is $45^\circ$ . Based on the above information, answer the following questions :
37 (ii) (b) $\Delta OPB$
Angle of Elevation Problems
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two Sections A and B. Tower is supported by wires from a point O. Distance between the base of the tower and point O is 36 cm. From point O, the angle of elevation of the top of the Section B is $30^\circ$ and the angle of elevation of the top of Section A is $45^\circ$ . Based on the above information, answer the following questions :
37 (iii) $Find the height of the Section A from the base of the tower.$
Angle of Elevation Problems

2022

11 q

8 $30^\circ$
Angle of Depression Problems
9 (a) $30^\circ$
Angle of Elevation Problems
8 $30^\circ$
Angle of Elevation Problems
9 $30^\circ$
Angle of Elevation Problems
9 (b) $30^\circ$
Angle of Depression Problems
12 $30^\circ$
Angle of Depression Problems
12 $60^\circ$
Angle of Elevation Problems
Kite Festival Kite festival is celebrated in many countries at different times of the year. In India, every year $14^{\text{th}}$ January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, shows three kites flying together. In Fig. 5, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $30^\circ$ and $60^\circ$ respectively. Taking AD = 50 m and BE = 60 m, find
13 (1) $the lengths of strings used (take them straight) for kites A and B as shown in the figure.$
Angle of Elevation Problems
Kite Festival Kite festival is celebrated in many countries at different times of the year. In India, every year $14^{\text{th}}$ January is celebrated as International Kite Day. On this day many people visit India and participate in the festival by flying various kinds of kites. The picture given below, shows three kites flying together. In Fig. 5, the angles of elevation of two kites (Points A and B) from the hands of a man (Point C) are found to be $30^\circ$ and $60^\circ$ respectively. Taking AD = 50 m and BE = 60 m, find
13 (2) $the distance ‘d’ between these two kites$
Angle of Elevation Problems
Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in $14^{\text{th}}$ century. The lake has many Chhatris. One of them is shown below : Observe the picture. From a point A $h$ m above from water level, the angle of elevation of top of Chhatri (point B) is $45^\circ$ and angle of depression of its reflection in water (point C) is $60^\circ$ . If the height of Chhatri above water level is (approximately) 10 m, then
14 (a) $draw a well-labelled figure based on the above information;$
Angle of Elevation Problems
Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in $14^{\text{th}}$ century. The lake has many Chhatris. One of them is shown below : Observe the picture. From a point A $h$ m above from water level, the angle of elevation of top of Chhatri (point B) is $45^\circ$ and angle of depression of its reflection in water (point C) is $60^\circ$ . If the height of Chhatri above water level is (approximately) 10 m, then
14 (b) $(h)$
Angle of Elevation Problems

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 3 times: 2023, 2024, 2026
9 $\sqrt{3}$
Tap an option to check your answer.
Question 2
Asked 3 times: 2022*, 2024*, 2026 (* = numbers or wording changed that year)
34 (b) $30^\circ$
Question 3
Asked 3 times: 2023*, 2024*, 2026 (* = numbers or wording changed that year)
12 $45^\circ$
Tap an option to check your answer.
Question 4
Asked 3 times: 2024*, 2025*, 2026 (* = numbers or wording changed that year)
34 (a) $30^\circ$
Question 5
Asked 3 times: 2022*, 2023*, 2024 (* = numbers or wording changed that year)
34 $30^\circ$
Question 6
Asked 3 times: 2022*, 2023*, 2024 (* = numbers or wording changed that year)
34 $30^\circ$
Question 7
Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)
32 $60^\circ$
Question 8 (case study, 4 parts)
Asked 2 times: 2023*, 2026 (* = numbers or wording changed that year)
Radio towers are used for transmitting a range of communication services including radio and television. The tower will either act as an antenna itself or support one or more antennas on its structure. On a similar concept, a radio station tower was built in two sections ‘A’ and ‘B’. Tower is supported by wires from a point ‘O’ (as shown in figure). Distance between the base of the tower and point ‘O’ is 6 m. From point ‘O’, the angle of elevation of the top of the section ‘B’ is $30^\circ$ and the angle of elevation of the top of section ‘A’ is $60^\circ$ . Based on the above information, answer the following questions :
37 (i) $Find the length of the wire from the point ‘O’ to the top of section ‘B’.$
37 (ii) $Find the length of the wire from the point ‘O’ to the top of section ‘A’.$
37 (iii) (a) $Find the distance AB.$
37 (iii) (b) $\Delta OPB$
Question 9
Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)
9 $30^\circ$
Tap an option to check your answer.
Question 10
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
35 (a) $45^\circ$

9.1 Heights and Distances

Solved Examples

Exercise 9.1

What the board has asked from this chapter

2026

2025

2024

2023

2022

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8 (case study, 4 parts)

Question 9

Question 10