A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 50°. If the string is 400 ft long, how high is the kite above the ground?
We can use trigonometry to solve this problem. Let's draw a diagram:
We want to find the height of the kite (h), which is the opposite side of the right triangle. The adjacent side is the length of the string (400 ft), and the angle opposite the height is 50°. We can use the tangent function:
tan(50°) = h/400
To solve for h, we can multiply both sides by 400:
400 tan(50°) = h
Using a calculator, we can find:
400 tan(50°) ≈ 514.9
Therefore, the kite is about 514.9 ft above the ground.