Trigonometry Word Problem

Question

An arborist wants to prune an oak tree that has grown too tall. The arborist takes a 15-foot ladder and places it on a horizontal surface on the ground so it leans against the tallest part of the tree trunk. If the bottom part of the ladder makes an angle of 70 degrees with respect to the ground, what is the distance between the ladder and the tree trunk? If necessary, round your answer to the nearest tenth of a foot.

Answer 1

Draw a picture and note that you have a right triangle with the length L of the ladder as hypotenuse, and the distance between the ladder and the tree trunk as the base.  Call the base b.  Then

 

b/L = cos70°

 

b = L cos70° = (15 ft)cos70° = ? ft