Question

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.)

Answer 1

Possible answers:

A)

≈ 2,339 ft

B)

≈ 23,301 ft

C)

≈ 22,159 ft

D)

≈ 7,570 ft

Answer 2

To find the horizontal distance, we need to apply trigonometry.

Let's denote the horizontal distance from the plane to the control tower as x.

We know that the angle of depression is 18°, which means that the angle between the horizontal line and the line of sight from the plane to the control tower is also 18°.

Now we can use the tangent function (tan) to find x:

tan(18°) = opposite/adjacent

In this case, the opposite side is the altitude of the plane, which is 7200 feet. The adjacent side is the horizontal distance x, which we want to find.

Using the formula:

tan(18°) = 7200/x

To solve for x, we can rearrange the equation:

x = 7200 / tan(18°)

Using a calculator:

x ≈ 24999.2 feet

Rounding to the nearest foot, the horizontal distance from the plane to the control tower is 25000 feet.

Answer 3

None of the options provided matches the calculated value.

Using the trigonometric equation:

x = 7200 / tan(18°)

x ≈ 24999.2 feet

Therefore, rounding to the nearest foot, the correct answer should be:

E) ≈ 25000 ft