To find the height of the lighthouse, we can create a right triangle with the lighthouse as the height, the distance from the base to the point where the angle is measured as the base, and the line of sight as the hypotenuse.
Given that the angle of elevation is 55 degrees and the base is 12.3m, we can use trigonometry to find the height of the lighthouse.
Let h be the height of the lighthouse. Using the tangent function, we have:
tan(55 degrees) = h / 12.3
Solving for h:
h = 12.3 * tan(55 degrees)
h = 12.3 * 1.4281
h ≈ 17.59m
Therefore, the height of the lighthouse is approximately 17.59 meters.
At a point 12.3m from the base of a lighthouse, the angle of elevation to the top of the lighthouse is 55 degrees. How tall is the lighthouse?
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