A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 11degrees
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. 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.
Let's assume that the horizontal distance from the boat to the lighthouse is x feet.
In a right triangle formed by the boat, the lighthouse, and the line of sight to the beacon, the angle of elevation is 11 degrees.
Using trigonometry, we can find the horizontal distance (x) using the tangent function:
tan(11 degrees) = opposite/adjacent
tan(11 degrees) = 139/x
To solve for x, we isolate it by multiplying both sides of the equation by x:
x * tan(11 degrees) = 139
x = 139 / tan(11 degrees)
Using a calculator, we find that tan(11 degrees) is approximately 0.193.
x = 139 / 0.193
x ≈ 719.32
Therefore, the ship's horizontal distance from the lighthouse (and the shore) is approximately 719.32 feet.