Explanation:
First, let's draw a diagram to visualize the problem:
B <-- bow of the boat
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| \ h = 120 ft (height of the lighthouse)
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L-------P
Don't laugh at my drawing anyway let's continue.
In the diagram, L represents the foot of the lighthouse, P represents the projection of the boat's position onto the horizontal plane, and h is the height of the lighthouse.
We know that the angle of depression from the top of the lighthouse to the bow of the boat is 26°. This means that angle BLP in the diagram is 26°.
We want to find the distance from the boat to the foot of the lighthouse, which is LP. Let's call this distance x.
We can use trigonometry to solve for x. In right triangle BLP, we have:
tan(26°) = h / x
Solving for x, we get:
x = h / tan(26°) = 245.79 ft
Therefore, the distance from the boat to the foot of the lighthouse is approximately 245.79 feet, rounded to the nearest foot...