Trigonometry question

Question

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

Answer 1

The distance from the top of the tree to your position (108 feet) forms the hypotenuse of the right triangle, while height of the tree to above you (above 5.75 feet) will be the side opposite the angle of elevation (66).

Using the sine function for the elevation angle (= opposite/hypotenuse):

sin(66) = height of tree above you/108 feet

108*sin(66) = height of tree above you

108*sin(66) + 5.75 = height of tree

Answer 2

Draw a figure.

h = 108 tan 66° + 5.75

You should be able to read this solution directly off of your figure!