Question

To approach the runway, a pilot of a small plane must begin a 5 degree descent starting from a height of 1266 feet above the ground. To the nearest tenth of a mile, how many miles from the runway is the airplane at the start of this approach?

Answer 1

2.8 miles

Explanation:

From the attached sketch of the solution diagram, let x = distance of plane from runway :

The sketch gives a right angled triangle ; hence, we can apply trigonometry :

To obtain x :

Sin θ = opposite / hypotenus

Sin 5 = 1266 / x

0.0871557 * x = 1266

x = 1266 / 0.0871557

x = 14525.720 feets

Converting feets to mile :

1 mile = 5280 feets

14525.720 feets = 14525.720 / 5280

2.751 miles

To the nearest tenth of a mile ; 2.8 miles