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

Angle of elevation is 35°

Explanation:

A child lies on the ground and looks up at the top of the tree which is 9 ft of height.

Child is 13 feet away so we have to calculate the angle of elevation from child to the top of the tree.

Let the angle of elevation is ∅ then

tan ∅ =
`(9)/(13)`

∅ =
`tan^(-1)((9)/(13))`

∅ =
`tan^(-1)(0.6923)`

∅ = 34.69° ≅ 35°

Therefore the angle of elevation is 35°

Answer 2

The angle of elevation : α
tan α = 9/13
tan α = 0.6923
α = tan^(-1) 0.6923
α = 34.69° ≈ 35°
Answer: the angle is 35°