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? (Round your answer to the nearest foot.)
We can use trigonometry to solve this problem. The angle of elevation is formed by the ground and the line of sight to the kite. Let's call the height of the kite h.
We can use the tangent function:
$$\tan(50^\circ) = \frac{h}{400}$$
Multiplying both sides by 400, we get:
$$h = 400\tan(50^\circ) \approx 547\text{ ft}$$
Rounding to the nearest foot, the kite is approximately 547 feet above the ground.