Question #1935

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?

Expert's answer

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

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

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