Question

A car is approaching a building. When it is 300 ft away, the angle of depression from the top of the building to the car is 42°. To the nearest foot, how tall is the building?

Answer 1

Answer: 333.2ft

Explanation:

We can draw a triangle rectangle, where the distance between the base of the building and the car is one cathetus (300ft)

The height of the building is the other cathetus.

Now, we know that the angle of depression from the top of the building to the car is 42°

This angle is measured from a perpendicular line in from the building, so the "top angle" of the triangle rectangle will be:

90° - 42° = 48°

if we steep on this angle, the 300ft cathetus is the opposite cathetus and the height of the building is the adjacent cathetus.

Here we can use the relation:

Tan(A) = Opposite cathetus/adjacent cathetus:

Then:

Tan(48°) = H/300ft

Tan(48°)*300ft = H = 333.2ft

Answer 2

270 ft

Explanation:

The angle of depression from the top of the building to the car = 42° and the distance from the car to the building is 300 ft.

This can be represented by a right triangle with:

Adjacent side to the angle = distance from the car to the building = 300 ft, opposite side to angle = height of building = x and angle (θ) = 42°

From trigonometry:

`tan(\theta)=(opposite)/(adjacent) \\Therefore:\\tan(42)=(x)/(300)\\ x = 300*tan(42)= 300*0.9\\x=270ft`

The height of the building is 270 ft