Question

Jon is in a raft 100m from the base of a 54m cliff. What is the angle of depression from the he top of the cliff to the raft? Let a = 54 and b = 100 Round answer to the nearest tenth

Answer 1

28.4 degrees

Explanation:

In the diagram attached

Height of the cliff, AB=54 m

Distance of the raft to the base of the cliff, AC=100m

We want to determine the angle of depression from the top of the cliff to the raft. This is angle OBA.

`\angle OBA = \angle BAC $ (Alternate Angles)\\Therefore, in the right triangle ABC\\\tan A =(BC)/(AC)\\ \tan A =(54)/(100)\\\tan A =0.54\\A=\arctan 0.54\\A=28.4^\circ$ (to the nearest tenth)`

The angle of depression from the top of the cliff to the raft is 28.4 degrees correct to the nearest tenth.