Question

SOMEONE HELP ME ASAP PLZZ!!!

Max is in a control tower at a small airport. He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27o. What is the distance of the plane from the base of the tower? Round to the nearest foot.

Answer 1

The distance of the plane from the base of the tower is 25.5 foot.

Explanation:

As given

Max is in a control tower at a small airport.

He is located 50 feet above the ground when he spots a small plane on the runway at an angle of depression of 27°.

Now by using the trigonometric identity.

`tan\theta = (Perpendicular)/(Base)`

As shown in the figure given below

Perpendicular = CB

Base = AC = 50 feet

`\theta = 27^(\circ)`

Put in the identity.

`tan\ 27^(\circ) = (CB)/(AC)`

`tan\ 27^(\circ) = (CB)/(50)`

`tan\ 27^(\circ) = 0.51\ (Approx)`

Put in the above

`0.51 = (CB)/(50)`

CB = 0.51 × 50

CB = 25.5 foot

Therefore the distance of the plane from the base of the tower is 25.5 foot.