Question

A plane is flying at an altitude of 13,100 ft. The angle of depression from the plane to a control tower is 12º. What is the horizontal distance from the plane to the tower? Answer rounded to the nearest tenth of a foot.

Answer 1

The horizontal distance from the plane to the control tower is 61630.7 ft.

Explanation:

Here we have that

Height of flight of plane = 13,100 ft = Opposite side of angle of elevation

Angle of depression from the plane to the control tower = 12°

Therefore, the control tower can be sighted on a straight (hypotenuse) line from the plane with an angle of depression of 12°

Angle of depression from the plane to the control tower = Angle of elevation from the control tower to the plane = 12°

Horizontal distance from the plane to the control tower = Adjacent side of the hypotenuse of the right triangle = (Opposite side of angle of elevation) ÷ (Tangent of angle of elevation)

∴ Horizontal distance from the plane to the control tower = 13,100/(tan(12°)

Horizontal distance from the plane to the control tower = 61630.7 ft. to the nearest tenth of a foot.

Answer 2

The horizontal distance from the plane to the tower is 2784.5 feet.

Explanation:

From the given question, the height of the control tower is not given. But;

Tan θ =
`(Opposite side)/(Adjacent side)`

Tan
`12^(0)` =
`(x)/(13100)`

x = 13100 × Tan
`12^(0)`

= 2784.4910

Thus, x = 2784.5 feet

Therefore, the horizontal distance from the plane to the tower is 2784.5 feet.