Question

The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.

1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft
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Answer 1

To solve this problem, we can use trigonometry. The tangent of the angle of elevation is equal to the height of the hill divided by the distance from point A to the base of the hill. So:

tan(49°) = height/400

height = 400 * tan(49°) = 459.3 ft (rounded to the nearest tenth)

Therefore, the answer is option 4) 459.3 ft

Answer 2

The hill is 460.1 feet tall, rounded to the nearest tenth. So, the correct option is (1).

This is a right triangle, where the side adjacent to the angle of elevation (400 feet) is the base and the side opposite the angle of elevation is the height we're trying to find.

We can use the tangent function (opposite over adjacent) to solve for the height.

tan(49°) = height / 400 feet

height = 400 feet * tan(49°)

height = 460.05 feet

Therefore, the hill is 460.1 feet tall, rounded to the nearest tenth.