Question

From the top of a lighthouse 240 feet high, the angle of depression to a boat out on the water is 23 degrees. Find the distance from the boat to the bottom of
the lighthouse. Round your answer to the nearest foot.

Answer 1

Answer:   565 feet

This value is approximate.

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Explanation:

Imagine you are at the top of the lighthouse, and look straight horizontally outward. Then imagine looking down 23 degrees to spot the boat. This forms the angle of depression.

The adjacent angle complementary to this is 90-23 = 67 degrees. This is the interior angle of the triangle needed, and this angle is at the top of the triangle.

tan(angle) = opposite/adjacent

tan(67) = x/240

x = 240*tan(67)

x = 565.4045677977 approximately

x = 565 feet

The diagram is below.