Question

A 254–foot tall radio tower is located partway between a building and a tree. The angle of elevation from the base of the building to the top of the tower is 36°, and the angle of elevation from the base of the tree to the top of the tower is 62°. What is the distance from the base of the building to the base of the tree (rounded to the nearest foot)?

Answer 1

485 ft

Explanation:

step 1

Find the distance from the base of the building to the base of the radio tower

Let

x -----> the distance from the base of the building to the base of the radio

we know that

tan(36°)=254/x

x=254/tan(36°)=349.60 ft

step 2

Find the distance from the base of the tree to the base of the radio tower

Let

x -----> the distance from the base of the tree to the base of the radio tower

we know that

tan(62°)=254/x

x=254/tan(62°)=135.05 ft

step 3

Find the distance from the base of the building to the base of the tree

Adds the distances

349.60 ft+135.05 ft=484.65 ft

Round to the nearest foot

484.65 ft=485 ft