word problem

Question

A surveyor standing 60 meters from the base of a building measures the angle to the top of the building and finds it to be 37°. The surveyor then measures the angle to the top of the radio tower on the building and finds that it is 49°. To the nearest hundredth, how tall is the radio tower?

Answer 1

Draw and label a diagram!

b represents height of the building

t represents the height of the tower

 

tan 37° = b / 60

0.753554050 ≈ b / 60

45.2132430 ≈ b

 

tan 40° = (b + t) / 60

0.839099631 ≈ (b + t) / 60

50.3459779 ≈ b + t

50.3459779 ≈ 45.2132430 + t

5.13273490 ≈ t