Question

An airplane pilot spots the control tower at an angle of depression of 47*. He knows that his altitude is 30,000 ft. What is the ground distance from the plane to the tower, to the nearest foot

Answer 1

The ground distance from the plane to the tower, to the nearest feet is 27975 feet.

Explanation:

An airplane pilot spots the control tower at an angle of depression of 47° i.e. the angle of elevation from the tower to the plane is 47°.

Now, the altitude of the plane is 30000 ft. from the ground.

So, the height of the right triangle is 30000 ft and the base of the right triangle i.e. ground distance from the tower to the plane is required to find out.

Hence,
`\tan 47 = \frac{\textrm {Height}}{\textrm {Base}} = (30000)/(x)` {Where the base is assumed to be x ft.}

⇒
`x = (30000)/(\tan 47) = 27975.45` feet.

Therefore, the ground distance from the plane to the tower, to the nearest feet is 27975 feet. (Answer)