Question

A boat heading out to sea starts out at Point AA, at a horizontal distance of 590 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 11degrees ∘ . At some later time, the crew measures the angle of elevation from point BB to be 2degrees ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer 1

Using trigonometry, we can determine the distance from point AA to point BB. By setting up an equation involving the tangent of the angle of elevation at point AA and the given distance from AA to the lighthouse, we can solve for the distance from AA to BB. Calculating the equation, we find that the distance from AA to BB is approximately 120.56 feet.

To find the distance from point AA to point BB, we can use trigonometry and the given angles of elevation.

Let's start by labeling the given information:

- Distance from point AA to the lighthouse: 590 feet

- Angle of elevation at point AA: 11 degrees

- Angle of elevation at point BB: 2 degrees

Using trigonometry, we can set up the following equation:

tan(11 degrees) = (distance from AA to BB) / 590 feet

To find the distance from AA to BB, we rearrange the equation:

(distance from AA to BB) = 590 feet * tan(11 degrees)

Calculating this using a calculator, the distance from AA to BB is approximately 120.56 feet.

Therefore, the distance from point AA to point BB is approximately 120.56 feet.