Question

A boat is heading towards a lighthouse, whose beacon-light is 119 feet above the

water. From point A, the boat's crew measures the angle of elevation to the beacon,
5°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 18°. Find the distance from point A to point B.
Round your answer to the nearest foot if necessary.

Answer 1

To find the distance from point A to point B, you can use the concept of trigonometry, specifically the tangent function. The equation tan(5°) = (119 ft) / (x ft) can be used to find the value of x, which represents the distance from point A to the lighthouse (point C). The distance from point A to point B is approximately 1367 feet.

Step-by-step explanation:

To find the distance from point A to point B, we can use the concept of trigonometry. Let's assume the distance from point A to the lighthouse (point C) is x feet. From point A, the angle of elevation to the beacon is 5°, and from point B, it is 18°.

Using the tangent function, we can set up the following equation:

tan(5°) = (119 ft) / (x ft)

Solving this equation, we find that x = (119 ft) / tan(5°) = 1367.31 ft (rounded to the nearest foot).