The distance from the helicopter to point P is denoted by x, and the height of the helicopter is denoted by h. In the right triangle formed by the helicopter, point P, and the point directly below the helicopter on the coast of the island, we can see that the angle of depression from the helicopter to point P is 41 degrees.
This implies that the angle between the height of the helicopter and the line connecting the helicopter to point P is also 41 degrees. Therefore, we can use the tangent function to determine the distance x.
Using the formula tan(41 degrees) = h/x, we find that x = 850/tan(41 degrees), which simplifies to approximately 977.8 feet. Thus, the distance from the helicopter to the island is approximately 977.8 feet.
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Let x be the distance from the helicopter to point P, and let h be the height of the helicopter.
We have a right triangle formed by the helicopter, point P, and the point directly below the helicopter on the coast of the island.
From the information given, the angle of depression from the helicopter to point P is 41 degrees. This means that the angle between the height of the helicopter and the line connecting the helicopter to point P is also 41 degrees.
Therefore, tan(41 degrees) = h/x
tan(41 degrees) = 850/x
x = 850/tan(41 degrees)
x ≈ 850/tan(41 degrees)
x ≈ 850/0.8692867376
x ≈ 977.84 feet
So, the distance from the helicopter to the island is approximately 977.8 feet.
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