Question

A boat heading out to sea starts out at Point AA, at a horizontal distance of 1315 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 12degrees

∘
. At some later time, the crew measures the angle of elevation from point BB to be 8degrees
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer 1

To find the distance from point AA to point BB, use trigonometry. Use the tangent function to find the height of the lighthouse, and then use that height and the tangent function again to find the horizontal distance between point AA and BB. The distance is approximately 1832 feet.

Step-by-step explanation:

To find the distance from point AA to point BB, we can use trigonometry. First, we need to find the height h of the lighthouse using the given angle of elevation. Since the angle of elevation is 12 degrees, we can use the tangent function to find h. tan(12) = h/1315. Rearranging the equation, we get h = 1315*tan(12). Next, we can find the horizontal distance x between point AA and BB using the height h and the angle of elevation at point BB. Since the angle of elevation at point BB is 8 degrees, we can use the tangent function again to find x. tan(8) = h/x.

Rearranging the equation, we get x = h/tan(8).

Substituting the value of h we found earlier, we get x = (1315*tan(12))/tan(8).

Evaluating this expression, we find that the distance from point AA to point BB is approximately 1832 feet.