Question

A jet is coming in for a landing. It's currently 25,000 feet in

the air and the landing strip is 45,000 feet directly ahead. In
order to ensure a safe landing the plane needs to come in at no
more than a 30° angle of depression. Will this be a safe
landing?
Is this a safe landing?

Answer 1

The angle of depression is 29.0521°. So it is a safe landing.

Explanation:

Step 1:

The plane is flying at a height of 25,000 feet and 45,000 feet away from the landing strip. Assume it lands with an angle of depression of x°.

So a right-angled triangle can be formed using these measurements. The triangle's opposite side measures 25,000 feet while the adjacent side measures 45,000 feet. The angle of the triangle is x°.

To determine the value of x, we calculate the tan of the given triangle.

`tanx = (opposite side)/(adjacent side).`

Step 2:

The length of the opposite side = 25,000 feet.

The length of the adjacent side = 45,000 feet.

`tan x = (25,000)/(45,000) = 0.5555.`

So x = 29.0521°. Since x < 30°, it is a safe landing.