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A monument stands 60 metres tall. From its peak, the angles of depression to the top and bottom of a nearby statue are 30° and 60°, respectively. Determine the approximate height of the statue and the horizontal distance separating the monument from the statue.

1. height = 25.4 m, distance = 60 m
2. height = 40 m, distance = 34.64 m
3. height = 30 m, distance = 40 m
4. height = 32 m, distance = 45 m

Correct answer: height = 40 m, distance = 34.64 m

Solution

Let the horizontal distance be \(d\). From the angle of depression to the bottom, \(\tan 60^\circ = 60/d\), so \(d = 60/\sqrt{3} \approx 34.64\) m. For the top of the statue, \(\tan 30^\circ = (60-h)/d\), which gives \(60-h = 20\), so \(h = 40\) m.

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