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Heights and Distances

SSC CGL Tier II Quant. Try each one first, then open its answer.

Top 10 SSC CGL Tier II PYQs to practise first

The questions and kinds of question asked most often come first. Each one says how often and in which papers.

  1. Question 1

    This type asked 3 times: 3 Mar 2023 Tier II, 6 Mar 2023 Tier II, 26 Oct 2023 Tier II. This one: 26 Oct 2023 Tier II See all 3 of this type

    2
    From the top of a tower, the angle of depression of the top of a 10 m high building is 60∘60^\circ. If the distance between the tower and the building is 50350\sqrt{3} m, find the height of the tower.

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  2. Question 2

    This type asked 2 times: 3 Feb 2022 Tier II, 26 Oct 2023 Tier II. This one: 26 Oct 2023 Tier II See all 2 of this type

    19
    Two pillars of equal height stand on either side of a roadway which is 150 m wide. At a point in the road between pillars, the elevations of the pillars are x∘x^\circ and y∘y^\circ so that tan⁡x∘=25,tan⁡y∘=35\tan x^\circ = \frac{2}{5}, \tan y^\circ = \frac{3}{5}, then the height of each pillar is:

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  3. Question 3

    This type asked 2 times: 8 Aug 2022 Tier II, 3 Mar 2023 Tier II. This one: 3 Mar 2023 Tier II See all 2 of this type

    11
    The angle of elevation of the top of a building at a distance of 70 m from its foot on a horizontal plane is found to be 60∘60^\circ. Find the height of the building.

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  4. Question 4

    This type asked 2 times: 29 Jan 2022 Tier II, 2 Mar 2023 Tier II. This one: 2 Mar 2023 Tier II See all 2 of this type

    27
    Two ships are on the opposite of a light house such that all three of them are collinear. The angles of depression of the two ships from the top of the light house are 30∘30^\circ and 60∘60^\circ. If the ships are 2303230\sqrt{3} m apart, then find the height of the light house (in m).

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  5. Question 5

    Asked once: 6 Mar 2023 Tier II (same type asked 3 times) See all 3 of this type

    25
    From the top of an upright pole 24324\sqrt{3} feet high, the angle of elevation of the top of an upright tower was 60∘60^\circ. If the foot of the pole was 60 feet away from the foot of the tower, what tall (in feet) was the tower?

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  6. Question 6

    Asked once: 3 Feb 2022 Tier II (same type asked 2 times) See all 2 of this type

    92
    Two pillars A and B of the same height are on opposite sides of a road which is 40 m wide. The angles of elevation of the tops of the pillars A and B are 30∘30^\circ and 45∘45^\circ, respectively, at a point on the road between the pillars. What is the distance (in m) of the point from the foot of pillar A?

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  7. Question 7

    Asked once: 8 Aug 2022 Tier II (same type asked 2 times) See all 2 of this type

    80
    An person 1.8 metre tall is 30330\sqrt{3} metre away from a tower. If the angle of elevation from his eye to the top of the tower is 30 degree, then what is the height (in m)of the tower?

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  8. Question 8

    Asked once: 29 Jan 2022 Tier II (same type asked 2 times) See all 2 of this type

    89
    The angle of elevation of the top of a tower 25325\sqrt{3} m high from two points on the level ground on its opposite sides are 45∘45^\circ and 60∘60^\circ. What is the distance (in m) between the two points (correct to one decimal place)?

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  9. Question 9

    Asked once: 3 Mar 2023 Tier II (same type asked 3 times) See all 3 of this type

    30
    From the top of an upright pole 17.75 m high, the angle of elevation of the top of an upright tower was 60∘60^\circ. If the tower was 57.75 m tall, how far away (in m) from the foot of the pole was the foot of the tower?

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  10. Question 10

    Asked once: 7 Mar 2023 Tier II

    4
    The angle of elevation of the top of a tower from the top of a building whose height is 680 m is 45∘45^\circ and the angle of elevation of the top of same tower from the foot of the same building is 60∘60^\circ. What is the height (in m) of the tower?

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