An airplane flying at an altitude of 7200 feet sights the angle of depression to a control tower to be
18°. Find the horizontal distance the plane is from the control tower. (Disregard the height of the
Tower and round your answer to the nearest foot.)

Question

Quizplus · Accepted Answer

We can use the tangent function to find the horizontal distance.
Let x be the horizontal distance.
tan(18°) = (height of tower)/(x)
tan(18°) = 7200/x
x = 7200/tan(18°)
x ≈ 21912
Rounding to the nearest foot, the horizontal distance is 21912 feet, which corresponds to choice B. Let the distance from the airplane to the control tower be x.
Then, we have:
tan 18° = opposite/adjacent = 7200/x
x = 7200/tan 18° ≈ 25,236
Rounding to the nearest foot gives x ≈ 25,236 ft. ≈ 25,236 feet.
Therefore, the horizontal distance the plane is from the control tower is approximately 25,236 feet, or answer B.

An Airplane Flying at an Altitude of 7200 Feet Sights