Discussion
The angle of elevation of the top of a lighthouse 60 m high, from two points on the ground on its opposite sides are 45° and 60°. What is the distance between these two points?
Answer: B
The two points are on opposite sides, so the lighthouse foot lies between them and their distances add.
\[ d_{45} = \frac{60}{\tan 45^{\circ}} = 60 \text{ m} \]
\[ d_{60} = \frac{60}{\tan 60^{\circ}} = \frac{60}{\sqrt{3}} = 20\sqrt{3} = 34.64 \text{ m} \]
\[ \text{total} = 60 + 34.64 = 94.64 \approx 94.6 \text{ m} \]
The larger angle gives the shorter distance, as expected - the steeper you have to look, the closer you are.
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