Trigonometric ratios

Question

What’s the horizontal distance between the point where an airplane begins to descend and where it lands if the plane descends at a 5° angle from an altitude of 7200ft?

Answer 1

Solution:

This forms a right angle triangle with a vertical side of 7200 ft, and an angle with the horizontal side of 5°. You are being asked to find the horizontal side of the triangle. The relation between the vertical and horizontal side is the tangent function, that is tan(5°) = opposite/adjacent, here the opposite side is the altitude of 7200 ft. , and the adjacent side is the horizontal distance needed lets call it x. Therefore,

tan(5°)=7200 ft, / x, rearrange by cross multiplication , then tan(5°) (x) = 7200 ft.

Divide both sides of the equation by tan(5°), you get x = 7200 ft. / tan(5°) = 82,296 ft.