NECO 2008 Mathematics · Question 32

Two ladders of length 5m and 7m lean against a pole and make angles 45° and 60° with the ground respectively…

Question

Two ladders of length 5m and 7m lean against a pole and make angles 45° and 60° with the ground respectively. What is their distance apart on the pole correct to two decimal places?

A.9.60m
B.6.06m
C.2.54m
D.2.53m
E.2.00m

Answer: D. 2.53m

Explanation written with AI and checked against the answer key

Analyze the question: Each ladder leans on the pole and touches it at a certain height. The height reached is found with the sine ratio. Their distance apart on the pole is the difference between the two heights. Concept: For a ladder of length L making angle θ with the ground, the height reached on the pole is h = L sin θ Solution: Ladder 1 (5 m, 45°): h₁ = 5 sin 45° = 5 × 0.7071 = 3.5355 m Ladder 2 (7 m, 60°): h₂ = 7 sin 60° = 7 × 0.8660 = 6.0622 m Distance apart on the pole: h₂ − h₁ = 6.0622 − 3.5355 = 2.5267 m ≈ 2.53 m Check against the options: 2.5267 rounds to 2.53, which matches option D. (Notice that 6.06 m, option B, is only the height of the 7 m ladder. It is a distractor for students who forget to subtract. Option C, 2.54, comes from rounding the intermediate values too early, for example 3.54 and 6.06 give 2.52, or 3.53 and 6.06 give 2.53, so keep at least 4 decimal places until the final step.) Tip: In "ladder and pole" problems, use sine for the height on the wall and cosine for the distance from the base. When asked for a difference, do not round until the very last step.

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