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

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Accepted Answer

1. Let horizontal distance be $x$ and statue height be $h$. Monument height is $60$ m.

2. Angle of depression to the top is $30^\circ$: $	an30^\circ=\dfrac{60-h}{x}=\dfrac{1}{\sqrt{3}}$, so $60-h=\dfrac{x}{\sqrt{3}}$.

3. Angle of depression to the bottom is $60^\circ$: $	an60^\circ=\dfrac{60}{x}=\sqrt{3}$, so $x=\dfrac{60}{\sqrt{3}}=20\sqrt{3}\approx34.64$ m.

4. Then $h=60-\dfrac{x}{\sqrt{3}}=60-\dfrac{20\sqrt{3}}{\sqrt{3}}=60-20=40$ m.

5. So the statue is $40$ m tall and the distance is about $34.64$ m. **Choice (b).**

FINAL_ANSWER: b

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