NECO 2005 Mathematics · Question 3

In Δ ABC, A = 60°, C = 90° and AC = 12m. Find the Length of the hypotenuse.

Options

A.24m
B.14m
C.12m
D.7m
E.6m

Answer: A. 24m

Explanation written with AI and checked against the answer key

Analyze the question Triangle ABC is right-angled at C, so the hypotenuse is AB (the side opposite the 90° angle). We know angle A = 60° and AC = 12 m. AC is the side adjacent to angle A. Concept In a right-angled triangle, cos θ = adjacent / hypotenuse. Solution For angle A = 60°: cos 60° = AC / AB 1/2 = 12 / AB AB = 12 × 2 = 24 m Check: Angle B = 30°, so this is a 30°-60°-90° triangle. The side opposite 30° (which is AC = 12) is half the hypotenuse, so the hypotenuse = 24 m. ✔ Answer: A. 24 m. Tip: In a 30°-60°-90° triangle, the sides are in the ratio 1 : √3 : 2. The shortest side (opposite 30°) is always half the hypotenuse. Also, remember SOH-CAH-TOA to decide quickly which ratio to use: here you have the adjacent side and want the hypotenuse, so use CAH (cosine).

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