SSC CGL 2025 Tier-I · 16 September 2025, Shift 2 · Quantitative Aptitude · Question 15 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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A tower stands 50 meters tall. From its peak, the angles of depression to the top and bottom of a nearby building are measured at 30° and 45°, respectively. Determine the approximate height of the building as well as the horizontal distance separating the tower from the building.

(a)height= 21 m , distance =50 m
(b)height = 25 m , distance = 25 m
(c)height = 28 m , distance = 15 m
(d)height = 18 m , distance = 15 m

Answer

Why

Correct — A. Stand at the tower's top, 50 m up, and use each angle of depression in turn.

To the building's foot, 45°:
tan 45° = 50 ÷ distance = 1
Distance = 50 m

To the building's top, 30°:
Drop below the tower top = 50 × tan 30° = 50 ÷ √3 ≈ 28.87 m

Building height = 50 − 28.87 ≈ 21.13 ≈ 21 m
Height 21 m, distance 50 m → option (a)

Why the others are wrong

(b)
height = 25 m , distance = 25 m — A 25 m distance fails the 45° sight line: tan 45° = 1, so the distance equals the full 50 m drop to the building's foot, not half of it.
(c)
height = 28 m , distance = 15 m — Height 28 m is roughly the 28.87 m drop from the tower top to the building's top, not the building's height. A 15 m distance also breaks tan 45° = 1.
(d)
height = 18 m , distance = 15 m — A 15 m distance cannot be right: at 45° the distance must equal the tower's 50 m height. The 18 m height does not match 50 − 50⁄√3 either.

Concept

An angle of depression is measured down from the horizontal at the observer's eye. By alternate angles it equals the angle of elevation from the object below, so each sight line makes a right triangle with the horizontal.

Both sight lines here share one horizontal distance. The 45° line fixes it at the tower's height, and the 30° line then gives how far the building's top lies below the tower's top.

Exact form: building height = 50 − 50⁄√3 = 50(√3 − 1)⁄√3 ≈ 21.13 m. The question asks for approximate values, which is why the option reads 21 m.

Key facts

tan 45° = 1, so at 45° the height and the horizontal distance are equal.
tan 30° = 1⁄√3 ≈ 0.577.
The angle of depression from the top equals the angle of elevation from below (alternate angles).

Study next

Two objects on opposite sides of a tower, seen at two angles of depressionAngles of elevation from two points on one line to the same towerValues of sin, cos and tan at 30°, 45° and 60°

Common traps

Taking 50 × tan 30° ≈ 28.87 m as the building's height instead of the drop from the tower's top.
Using tan 30° = √3 instead of 1⁄√3, which gives a drop of about 86.6 m, more than the tower's own height.

18 Sep 2025, 09:00, Quant Q.10 uses the same two angles from a 120 m tower to cars on opposite sides: the distances are 120 m and 120√3 m, so the cars stand 120(√3 + 1) m apart.

Related PYQs

No directly related past PYQ was found.

Topic: Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances — all 131 SSC CGL questions on it, every solved shift.