Question

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. What is the distance of the plane from the base of the tower? Round to the nearest foot. A. 25 feet B. 110 feet C. 56 feet D. 98 feet

Answer 1

tanα=y/x

x=y/tanα, we are told the height is 50 ft and the angle is 27°

x=50/tan27° ft

x≈98 ft (to nearest whole foot)

Answer 2

The distance of the plane from the base of the tower is:

Option: D

D. 98 feet

Explanation:

Let x denotes the distance of the plane from the base of the tower.

Now, in the right angled triangle we will need to use trignometric identity corresponding to 63°.

Based on the figure we have:

`\tan 63=(x)/(50)\\\\\\x=50* \tan 63`

`x=50* 1.9626\\\\\\x=98.13\ feet`

which to the nearest feet is:

98 feet