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A boat is heading towards a lighthouse, whose beacon-light is 135135 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 4∘4^\circ. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.

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Full solution

Q. A boat is heading towards a lighthouse, whose beacon-light is 135135 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 4∘4^\circ. What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
  1. Identify Relationship: Identify the relationship between the angle of elevation, the height of the lighthouse, and the horizontal distance. Use the tangent function because it relates opposite side (height of the lighthouse) to adjacent side (horizontal distance).
  2. Convert to Radians: Convert the angle from degrees to radians for calculation, since trigonometric functions in calculators often require radians. However, most modern calculators can compute directly in degrees, so this step is unnecessary here. Calculate the horizontal distance using the tangent function.
  3. Calculate Horizontal Distance: Perform the calculation using a calculator. Ensure the calculator is set to degree mode.

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