WAEC 2016 Mathematics · Question 18

Kweku walked 8m up to slope and was 3m above the ground. If he walks 12m further up the slope, how far above the ground will he be?

Options

A.4.5m
B.6.0m
C.7.5m
D.9.0m

Answer: C. 7.5m

Explanation written with AI and checked against the answer key

Analyze the question: Kweku walks along a straight slope. After 8 m along the slope, he is 3 m above the ground. We want his height after he walks a further 12 m along the slope, so the total distance along the slope is 8 + 12 = 20 m. Concept: On a straight slope, the height gained is proportional to the distance walked along the slope. This is because the angle of the slope stays the same, so height = distance × sin θ and sin θ is constant. Solution: From the first part: sin θ = 3/8 For the total distance of 20 m: height = 20 × (3/8) = 60/8 = 7.5 m You can also use proportion: 8 m → 3 m 20 m → h h = (20 × 3)/8 = 7.5 m Check: The 12 m extra gives 12 × 3/8 = 4.5 m of additional height. Then 3 + 4.5 = 7.5 m. This matches the working above. Answer: His total height above the ground is 7.5 m, which is option C. Tip: Watch the wording "walks 12 m further". Many students stop at 4.5 m (option A), which is only the extra height gained. The question asks for the total height above the ground, so add the first 3 m.

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