An airplane rises at an angle of 14 degrees with the ground.  Find to the nearest foot the distance it has flown when it has covered a horizontal distance of 1500 feet.

Expert Answers
ncchemist eNotes educator| Certified Educator

We have a right triangle where the bottom length is 1500 feet, the hypotenuse is the distance flown by the plane, and the angle between them is 14 degrees.  We know that for a right triangle, the cosine of the angle theta is equal to the adjacent side over the hypotenuse.  Looking at this mathematically:

`cos theta = (adjacent) / (hypotenuse)`

We want to solve for the hypotenuse:

`hypotenuse = (adjacent)/(cos theta)`

Plugging in the values:

`hypotenuse = (1500 feet)/(cos14)`

hypotenuse = 10969.95 feet

So the distance the plane has flown to the nearest foot is 10,970 feet.