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Math Asked by a SnapAndSolve user · about 2 hours ago

A boat is 200 feet from shore. The angle its line of sight makes with pier A relative to the shoreline is...

A boat is 200 feet from shore. The angle its line of sight makes with pier A relative to the shoreline is 35°. The angle its line of sight makes with pier B relative to the shoreline is 75°. How far is pier A from pier B rounded to the nearest foot?

Answer

To find the distance between pier A and pier B, we can use the Law of Sines in the triangle formed by the boat, pier A, and pier B.

  1. Let the distance between pier A and pier B be denoted as c.
  2. Using the Law of Sines:
    c / sin(70°) = 200 / sin(75°)
  3. Calculate sin(70°) and sin(75°):
    sin(70°) ≈ 0.9397
    sin(75°) ≈ 0.9659
  4. Substitute the values:
    c / 0.9397 = 200 / 0.9659
  5. Solve for c:
    c = (200 * 0.9397) / 0.9659 ≈ 194.3
  6. Rounded to the nearest foot, the distance between pier A and pier B is 194 feet.

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