WAEC 2024 Mathematics · Question 24

A ladder 15 m long leans against a vertical pole, making an angle of 72º with the horizontal. Calculate…

Question

A ladder 15 m long leans against a vertical pole, making an angle of 72º with the horizontal. Calculate, correct to one decimal place, the distance between the foot of the ladder and the pole.

A.15.8 m
B.14.3 m
C.4.9 m
D.4.6 m

Answer: D. 4.6 m

Explanation written with AI and checked against the answer key

Analyze the question: The ladder (15 m) is the hypotenuse of a right-angled triangle. The pole is vertical and the ground is horizontal. The ladder makes 72° with the horizontal. We need the distance from the foot of the ladder to the pole, which is the horizontal side, adjacent to the 72° angle. Concept: Cosine relates the adjacent side to the hypotenuse: cos θ = adjacent / hypotenuse Solution: cos 72° = d / 15 d = 15 × cos 72° cos 72° ≈ 0.3090 d = 15 × 0.3090 = 4.635 ≈ 4.6 m Check: The height up the pole would be 15 sin 72° ≈ 14.3 m (this is option B, the distractor for the wrong side). The distance along the ground must be shorter than the ladder, and with such a steep angle it should be small, so 4.6 m makes sense. Also, 4.6² + 14.3² ≈ 21.2 + 204.5 ≈ 225.7, close to 15² = 225, so it is consistent. Tip: Draw the triangle and label the sides relative to the given angle. "Distance from the pole along the ground" is the side next to the angle, so use cosine (CAH in SOH-CAH-TOA). If the question asked for the height reached on the pole, you would use sine instead. Option B is the trap for that mix-up.

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