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?

The car travelled 87ft.

Step-by-step 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.

the sum of all the angles in a triangle are equal to 180

so you can add   the 3 given angles together to equal 180:

5y + 2y + 2y = 180

or since all three angles have the same letter, combine the 3 angles to equal 180:

9y = 180