Question

Autumn measures the angle of elevation from the ground to the top of an 18-foot tall tree as 27°. To the nearest tenth of a foot, how far is she from the tree?

Answer 1

Answer: she is 35.3 feet from the tree.

Explanation:

Assuming her line of sight to the top of the tree is a straight line, then a right angle triangle is formed. The height of the tree, h represents the opposite side of the right angle triangle. Her distance, h from the tree represents the adjacent side of the right angle triangle. To determine h, we would apply the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan 27 = 18/h

h = 18/tan27 = 18/0.51

h = 35.3 feet