Problem

A boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. From point A, the boat's crew measures the angle of elevation to the beacon, 12∘, before they draw closer. They measure the angle of elevatiol a second time from point B at some later time to be 25∘. Find the distance from point A to point B. Round your answer to the nearest foot if necessary

Answer

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Answer

323 feet is the distance between point A and point B.

Steps

Step 1 ：Let the distance from point A to the lighthouse be x and the distance from point B to the lighthouse be y. We have the following equations:

Step 2 ：tan⁡(12∘)=126x

Step 3 ：tan⁡(25∘)=126y

Step 4 ：Solve the equations for x and y:

Step 5 ：x=126tan⁡(12∘)≈592.78

Step 6 ：y=126tan⁡(25∘)≈270.21

Step 7 ：Find the distance between points A and B, which is x−y:

Step 8 ：x−y≈592.78−270.21≈322.57

Step 9 ：323 feet is the distance between point A and point B.

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