Question

You are measuring theheight of a tree. You stand 40 feet from the base of the tree. The angle of elevation from your feet to the top of the tree is 65°.a. Make a creative, hand drawn sketch of the situation.b. Find the height of the tree to the nearest hundredth.

Answer 1

Okay, here we have this:

Considering the provided information, we are going to sketch the situation and find the height, so we obtain the following:

a)

b)

To calculate the height of the tree then we will use the trigonometric ratios, therefore since we know an angle, the adjacent leg and we want to know the opposite leg, then we will use the tangent ratio that relates these three measures:

tan(65°)=height/40ft

height=tan(65°)*40ft

height=85.78 ft

Finally we obtain that the height of the tree is approximately 85.78 feet.