SSC CGL 2024 Tier-I · 11 September 2024, Shift 2 · Quantitative Aptitude · Question 9 of 100

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 6 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

In a triangle ΔABC, the ∠ABC = 90°. If sin(A) = 1⁄2, then cos(C) is equal to:

Answer

Why

Correct — D. The stem and the options are images: the question gives ∠ABC = 90° and sin A = 1⁄2, and the four choices read 1, √3⁄2, 1⁄√2 and 1⁄2.

∠ABC names the angle at B, the middle letter, so the other two angles share what is left:
∠A + ∠C = 180° − 90° = 90°

So C = 90° − A, and by the complementary-angle identity:
cos C = cos(90° − A) = sin A = 1⁄2 → option (d).

The long route agrees: sin A = 1⁄2 gives A = 30°, so C = 60°, and cos 60° = 1⁄2.

Why the others are wrong

(a)
1 is cos 0°, and no angle of this triangle is 0°. With the right angle at B and A = 30°, the third angle is 60°, which is as far from 0° as the figure allows.
(b)
√3⁄2 is cos 30° — the cosine of the wrong angle. sin A = 1⁄2 fixes A at 30°, but the question asks for cos C, and C is the other acute angle.
(c)
1⁄√2 is cos 45°, which would need both acute angles to be 45°. That is the case sin A = 1⁄√2, not the given sin A = 1⁄2.

Concept

In a right-angled triangle the two acute angles always add to 90°, because the right angle has already used up half the 180°.

That makes them complementary, and complementary angles swap sine for cosine: cos(90° − θ) = sin θ and sin(90° − θ) = cos θ.

So in a right triangle the cosine of one acute angle is the sine of the other — no angle needs to be identified at all. Reading the answer straight off sin A is the one-line route.

The three-letter name does the hiding. ∠ABC is the angle at B, the middle letter, not the angle at A.

Read it as the angle at A and every line after it is wrong, which is why SSC writes the angle in three letters rather than one.

Key facts

The two acute angles of a right-angled triangle are complementary, adding to 90°.
cos(90° − θ) = sin θ, and sin(90° − θ) = cos θ.
sin 30° = 1⁄2 and cos 60° = 1⁄2.
In the three-letter notation ∠ABC, the vertex is the middle letter, B.

Study next

The complementary-angle relations for all six trigonometric ratiosRecovering the third side by Pythagoras once one acute angle is knownTrigonometric ratios read directly as side ratios of a right triangle

Common traps

Taking ∠ABC as the angle at A
Computing cos A instead of cos C
Reading sin A = 1⁄2 as A = 60° by confusing sin 30° with sin 60°

This is SSC's shortest trigonometry type: fix one acute angle from a standard value, then ask for a ratio of the other. Quant Q.8 in this same shift runs the long version — a bracket of standard-angle values divided by a compound-angle expression.

Related PYQs

No directly related past PYQ was found.