the angle of elevation from a ship to a 135-foot-tall lighthouse is 2 degrees. How far is the ship from the lighthouse?
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To find the distance between the ship and the lighthouse, we can use the tangent function. The tangent of an angle is equal to the opposite side divided by the adjacent side of a right triangle.
In this case, the opposite side is the height of the lighthouse (135 feet), and the angle of elevation is 2 degrees. We want to find the adjacent side, which represents the distance between the ship and the lighthouse.
The formula for the tangent function is:
tan(angle) = opposite / adjacent
Substituting the given values into the formula:
tan(2 degrees) = 135 feet / adjacent
Now, we can solve for the adjacent side:
adjacent = 135 feet / tan(2 degrees)
Using a scientific calculator, calculate the tangent of 2 degrees:
tan(2 degrees) ≈ 0.03492
Substituting this value back into the formula:
adjacent = 135 feet / 0.03492
Calculating this expression:
adjacent ≈ 3870.68 feet
Therefore, the ship is approximately 3870.68 feet away from the lighthouse.