Question

A boat is heading towards a lighthouse, whose beacon-light is 111 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 5º, before they draw closer. They measure the angle of elevation a second time from point B at some later time to be 15°. Find the distance from point A to point B. Round your answer to the nearest tenth of a foot if necessary.​

Answer 1

Answer: 854.5

Explanation:

I got it wrong so it gave me the explanation

Answer 2

The distance between point A and point B is approximately 854.39 feet.

How do we calculate the distance between point A and point B?

The distance between points A and B can be found using trigonometry. We shall denote the distance from point A to the lighthouse as x.

Using the tangent function:

tan(θ) = Opposite / Adjacent

For point A:

tan(5°) = 111/x

x = 111/tan(5°)

x ≈ 111 / 0.0875

x ≈ 1,268.57 feet (rounded to the nearest tenth)

Point B:

We shall also denote the distance from point B to the lighthouse as x

tan(15°) = 111/x

x = 111 / 0.268

x = 414.17 (rounded to the nearest tenth)

So, the distance between point A and point B is the difference between their distances to the lighthouse.

Distance = point A - point B

Distance = 1, 268.57- 414.18

Distance = 854.39 feet (rounded to the nearest tenth)

Hence, the distance between point A and point B is ≈ 854.39 feet.