SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · Quantitative Aptitude · Question 9 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 11 September 2026.

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A rock climber uses a rope to ascend a cliff. If the vertical height of the cliff is 35 meters and the rope makes an angle of 30° with the level ground, what is the minimum length of the rope required to reach the top?

(a)35m
(b)40m
(c)60m
(d)70m

Answer

Why

Correct — D. The cliff, the ground and the rope form a right triangle. The 35 m height is opposite the 30° angle, and the rope is the hypotenuse.

Pick the ratio: sin 30° = opposite ⁄ hypotenuse
Substitute: 1⁄2 = 35 ⁄ L
Multiply both sides by 2L: L = 35 × 2 = 70 m → option (d).

Why the others are wrong

(a)
35m — 35 m is the height itself, the vertical side. A rope slanting at 30° is the hypotenuse, which is always longer than either other side of a right triangle.
(b)
40m — 40 m is roughly 35 ⁄ cos 30° ≈ 40.4 m, the result of putting the 30° at the top of the cliff. The angle is with the ground, so the height is opposite it and sin applies.
(c)
60m — 60 m is close to 35√3 ≈ 60.6 m, the horizontal distance from the rope's foot to the cliff base. That is the adjacent side, found with tan 30°, not the rope.

Concept

In height-and-distance questions, name the three sides against the given angle first: opposite (the height), adjacent (along the ground) and hypotenuse (the slant: rope, ladder, wire).

Then pick the ratio that links the side you know to the side you want. Height known, slant wanted: sin. Ground distance known, slant wanted: cos. Height and ground distance: tan.

sin 30° = 1⁄2, so here the rope is exactly twice the height.

The rope is shortest when it runs straight from the ground to the top, so that straight line, the hypotenuse, is the minimum length the stem asks for.

Key facts

sin 30° = 1⁄2, cos 30° = √3⁄2 and tan 30° = 1⁄√3.
In a 30°-60°-90° triangle the sides are in the ratio 1 : √3 : 2, so the hypotenuse is twice the side opposite 30°.
Here the horizontal distance from the rope's foot to the cliff base is 35√3 ≈ 60.6 m.

Study next

Angles of elevation of one top from two points on the same lineLadder or wire questions that give the distance along the ground and need cosShadow-length questions at 30°, 45° and 60°

Common traps

Solving tan 30° = 35 ⁄ d for the ground distance d ≈ 60.6 m and reporting it as the rope.
Placing the 30° at the top of the cliff and using cos 30°, which gives about 40.4 m.

17 Sep 2025, 16:00, Quant Q.9 is the cos version: a wire fixed 10 m from a pole's base at 60° to the ground, keyed 20 m (10 ⁄ cos 60°).

A 45° shadow question also appears at Quant Q.15 of this shift, keyed 40 m.

Related PYQs

No directly related past PYQ was found.

Topic: Trigonometric ratio, Degree and Radian Measures, Standard Identities, Complementary angles, Heights and Distances — all 98 SSC CGL questions on it, every solved shift.