Question

From the top of a vertical cliff which is 7.9m tall, a boat has an angle of depression of 32°. How far, to the nearest metre is the boat from the base of the cliff?

Answer 1

13 m

Explanation:

assume x is the distance between the boat and the base of the cliff

By using the alternate interior angle theorem, we can know that the angle of elevation from the boat to the top of the vertical cliff is also 32°.

And since its opposite side is 7.9m, we can use trigonometry to find the answer (tangent = opposite / adjacent)

That is: 7.9 / x = tan32°

Transfer, we get: x = 7.9 / tan32° ≈ 12.64 ≈ 13 m