Answer: About 513 feet
A more accurate value is roughly 512.575960394824
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Explanation:
With many trig problems, a diagram should help steer you in the right direction. See below.
The red angle is the angle of depression. It's formed by starting off looking straight horizontal, then we look down 26 degrees. The blue angle adds to the red angle to get 90, so we can see that 26+64 = 90. Or you could say 90-26 = 64.
The goal is to find the value of x, which is the length from B (the lighthouse base) to point C (the ship's location).
The lighthouse is 250 ft tall, meaning AB = 250
We'll use angle BAC, or angle A for short, as the reference angle. This is the blue angle in the diagram.
We have a known adjacent side (AB = 250) and an unknown opposite side (BC = x). We use a tangent ratio to tie these sides together with the reference angle in question. This way we can solve for x.
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tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(64) = x/250
250*tan(64) = x
x = 250*tan(64)
x = 512.575960394824
x = 513
The distance from B to C is roughly 513 feet.
I'm rounding to the nearest whole number because the other values given to you are whole numbers.
