Question

From the top of a 150-ft building, Polly observes Tony driving a car toward her.

If the angle of depression to the car changes from 18 deg to 42 deg during the
observation, how far does the car travel?

Answer 1

The car travelled 87ft.

Explanation:

A) Let the distance between his initial position and the building be 'a'

Height of the building = 150ft

Angle of depression= 42°

tan 42° = a/150

0.90 = a/150

0.90 x 150 = a

a = 135ft.

B) Let the distance between the building and the final position of Tony be 'b'

Height of the building = 150ft.

Angle of depression = 18°

tan 18° = b/150

0.32 = b/150

0.32 x 150 = b

b = 48ft

The distance the car travelled = a - b

= 135 - 48

= 87 ft.

The car travelled 87ft.