SSC CGL Maths · Free notes
Heights and Distances: SSC CGL Quantitative Aptitude
Heights and Distances has 20 questions in the SSC CGL Tier I bank, and 18 of them come from the 2025 shifts. Thirteen are EASY, seven MODERATE and none HARD. Every row uses only 30°, 45° and 60°, so the trigonometry is three tangents and two special triangles. The real skill is reading the words into the right triangle: which side is the height, which is the ground distance, and whether a given length is the slant side. Once the picture is right, each question is one or two lines of working.
The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.
Subtopic notes
One Line of Sight
10 PYQsOne right triangle: an object's height, a distance along the ground and the angle between them, or a ladder, rope or wire that is the slant side.
Two Angles of Elevation or Depression
10 PYQsTwo right triangles that share a side: two observers looking at one tower, or one observer looking at two points, with the shared height or distance tying them together.
Formula & revision sheet
5 formulas · 14 gotchas across all subtopics — the exam-eve cheat-sheet
Formula & revision sheet
5 formulas · 14 gotchas across all subtopics — the exam-eve cheat-sheet
Formulas (2)
Watch out for (6)
- Measuring the angle of depression from the vertical→ Height and ground distance from one angle
- Swapping the 30° and 60° ratios→ Height and ground distance from one angle
- Expecting an exact answer when the options are rounded→ Height and ground distance from one angle
- Using tan when the slant length is given→ A ladder, rope or wire as the slant side
- Reading the angle with the wall as the angle with the ground→ A ladder, rope or wire as the slant side
- Rounding too early when the answer is to the nearest metre→ A ladder, rope or wire as the slant side
Formulas (3)
Watch out for (8)
- Subtracting the distances for observers on opposite sides→ Two observers on opposite sides of a tower
- Leaving a surd in the bottom when matching options→ Two observers on opposite sides of a tower
- Giving the larger angle to the farther point→ Two observers on the same side of a tower
- Using the 30° and 60° shortcut for other angles→ Two observers on the same side of a tower
- Treating two printed forms as different answers→ Two observers on the same side of a tower
- Taking the average of the two distances→ Complementary angles from two points
- Giving the building the height of the drop→ One observer reading two angles on the same vertical line
- Using the wrong angle for the shared distance→ One observer reading two angles on the same vertical line
PYQ weightage by concept
6 concepts · 20 PYQs — where the marks actually sit, so you know what to drill first
PYQ weightage by concept
6 concepts · 20 PYQs — where the marks actually sit, so you know what to drill first
| Concept | PYQs | Share |
|---|---|---|
| A ladder, rope or wire as the slant side | 6 | 30% |
| Height and ground distance from one angle | 4 | 20% |
| Concept | PYQs | Share |
|---|---|---|
| Two observers on opposite sides of a tower | 4 | 20% |
| Two observers on the same side of a tower | 3 | 15% |
| One observer reading two angles on the same vertical line | 2 | 10% |
| Complementary angles from two points | 1 | 5% |
Test yourself on Heights and Distances
10 past SSC CGL questions from this chapter, timed at 6 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.