A helicopter hovers 1250 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is 37 degrees.How far off the coast, to the nearest foot, is the island?
(Round the answer to the nearest whole number.
Using trigonometry, we can calculate the distance from the helicopter to the island.
We can see that the angle of depression is 37 degrees, so the angle between the coast and the line extending from the helicopter to the island is also 37 degrees.
Let x be the distance from the coast to the point where the line from the helicopter meets the coast. Using the tangent function, we can set up the equation:
tan(37 degrees) = 1250 / x
Solving for x:
x = 1250 / tan(37 degrees)
x ≈ 1592 feet
Therefore, the island is approximately 1592 feet away from the coast.