Matt wants to measure the height of a tree. he walks exactly 100 feet from the base of the tree and looks up. the angle from his eyes to the top of the tree is 35 ° . if his eye level is 5 feet from the ground, what is the height of the tree?

The height of the tree from the ground is 75 ft

Step-by-step explanation:

Let

h > the height of the tree from Matt's eye level

we know that

The tangent of angle of 35 degrees is equal to divide the opposite side to the angle of 35 degrees ( height of the tree from Matt's eye level) by the adjacent side to the angle of 35 degrees (100 feet)

so

tan(35°)=h/100

Solve for h

h=(100)tan(35°)=70 ft

Find the height of the tree from the ground

we know that

The height of the tree from the ground is equal to the height of the tree from Matt's eye level plus 5 feet

so

70+5=75 ft

both equations and proportions are better.