Question

To approach the runway, a pilot of a small plane must begin a 15 degree descent starting from a height of 2530 feet above the ground. how many miles from the runway is the airplane at the start of the approach

Answer 1

1. Let A represent the initial position of the plane and C the runaway (check the picture at the bottom of the answer).

2. The angle shown in the circle and angle C are alternate internior angles, or Z angles, so the measure of angle C is 15°.

3.
`tan 15^o= (2530)/(BC)`

4. Angle 15° is generally handled with half angle formulas, we have


`tan( (x)/(2)) = \sqrt{ (1-cosx)/(1+cosx)}`

so


`tan( (30)/(2)) = \sqrt{ (1-cos30)/(1+cos30)}= \sqrt{ (1- √(3)/2 )/(1+ √(3)/2)} = \sqrt{ (2- √(3) )/(2+ √(3) )} = \sqrt{ (0.268)/(3.732)}= √(0.072) =0.27`

5. Another way is to use a trigonometric values calculating software.

6. Thus,
`BC=2530/tan15^o=2530/0.27=9370 (ft)`