Question

A child lies on the ground and looks up at the top of a 9-ft tree nearby. The child is 13 ft away from the tree. What is the angle of elevation from the child to the top of the tree? Round to the nearest whole degree.

Answer 1

34.7° (rounded up to the nearest tenth)

Explanation:

The tree is 9 ft tall

The child is 13 ft away from the tree

The tree makes a right angle with the ground

`(9 ft)/(13 ft)` = Tan of angle of elevation from the child to the top of the tree

Let the angle of elevation be x°

So,

tan x° =
`(9 ft)/(13 ft)`

x° =
`tan^(-1)` 0f
`(9 ft)/(13 ft)` = 34.69515353°

Or 34.7° (answer rounded up to the nearest tenth)