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When the Sun’s elevation rises from 30° to 60°, the length of a tower’s shadow decreases by 60 m. The tower’s height is approximately:

1. 62 m
2. 101 m
3. 52 m
4. 301 m

Correct answer: 52 m

Solution

Shadow at 30deg is h*cot30 = h*sqrt(3); at 60deg it is h*cot60 = h/sqrt(3). The decrease is h*sqrt(3) - h/sqrt(3) = h*(2/sqrt(3)) = 60, so h = 30*sqrt(3) ~= 52 m.

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