Answer to Question #1935 in Trigonometry for Neil Horne

Question

A student stands a certain distance from a building and measures the angle to the top of the building as 18.8 degrees. The student then walks 24 ft straight towards the building and measures the angle to the top of the building as 20.2 degrees.
a) What is the height of the building, and
b) How close was the student to the bottom of the building after she had walked the 24 ft?

Answer 1

Denote the height of the building as H and the final distance from it as X, thus& the initial distance is X+24.
sin 18.8 = H/(X+24) and
sin 20.2 = H/X

Let's solve the system of equations:
0.322(X+24) = H
0.345X = H

0.322(X+24)& = 0.345X
0.023X = 7.728

The distance from the building is X = 336 ft
The height of the building is H = 0.345*336 = 115.92 ft