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.
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.