Question

The angle of depression from the top of a lighthouse to the base of a boat out at sea is 10°. If the lighthouse is at the

edge of land and is 82 meters tall, approximately how far out at sea is the boat?

15 m
176 m
465 m
711 m

Answer 1

Option C (465 meters).

Explanation:

This question can be solved using one of the three trigonometric ratios. The height of the lighthouse mentioned is 82 meters and the angle of depression is 10°. It can be seen that the required distance is given by x meters. This forms a right angled triangle, as it can be seen in the diagram. The perpendicular is given by 82 meters, the base is unknown, and the angle of 10° is given, as shown in the attached diagram. Therefore, the formula to be used is:

tan θ = Perpendicular/Base.

Plugging in the values give:

tan 10 = 82/x.

x = 82/tan 10.

x = 465.045109209 meters .

Therefore, the boat is 465 meters (to the nearest meters) far out in the sea. Therefore, the answer is Option C!!!