Question

A boat heading out to sea starts out at Point A, at a horizontal distance of 639 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 11 degrees . At some later time, the crew measures the angle of elevation from point B to be . Find the 3 degrees distance from point A to point B. Round your answer to the nearest foot if necessary .

Answer 1

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Answer:

  1731 ft

Step-by-step explanation:

The tangent relation is useful in this problem.

  Tan = Opposite/Adjacent

The height of the light is found to be ...

  tan(11°) = height/(639 ft)

  height = (639 ft)·tan(11°) . . . . . solve for height

Then the distance from the light to point B is ...

  tan(3°) = height/(B distance)

  B distance = height/tan(3°) = (639 ft)·tan(11°)/tan(3°) ≈ 2370 ft

Then the distance from point A to point B is ...

  2370 ft -639 ft = 1731 ft . . . AB distance