What is the angle of depression from the hiker's eyes to the base of the tree?

Question

A hiker is standing on a vertical cliff looking down at the base of a tree. The height of the cliff is 765 ft, and the tree is 515 ft from the base of the cliff. What is the angle of depression from the hiker's eyes to the base of the tree? 

 

A.The angle of depression is 56.05 .
 
B.The angle of depression is 47.69 .
 
C.The angle of depression is 42.31 .
 
D.The angle of depression is 33.95

Answer 1

Think of a triangle. The height of the trianle is 765 and the base of the triangle is 515. This is a right angle triangle so you can use trignometric functions to find the angle of depression.

 

From S(oh)C(ah)T(oa) we can use T(oa) to find the angle of depression as shown below:

 

Θ=tan^-1(515/765) = 33.95 (Answer D)

 

We used tangent and the opposite would be the base, since you are trying to find the angle of depression (looking down).