Question

you are looking at the top of a tree. The angle of elevation is 66 degrees. The distance from the top of the tree to your position is 108 feet. If you are a 5.75 feet tall, how tall is the tree (round to the nearest hundredth)

Answer 1

103! 108 divided by 5.75 = 102.25

Answer 2

Explanation:

A right angle triangle is formed. The distance from the top of the tree to your position represents the hypotenuse of the right angle triangle. The height of the tree represents the opposite side of the right angle triangle.

The height of the tree from the ground is the sum of the length of the opposite side and your height.

To determine the length of the opposite side, h, we would apply the Sine trigonometric ratio.

Sinθ = opposite side/hypotenuse Therefore,

Sin 66 = h/108

h = 108Sin66 = 108 × 0.9135

h = 98.66

Therefore, height of tree is

98.66 + 5.75 = 104.41 feet