A helicopter hovers 1250 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is 47 degrees.How far off the coast, to the nearest foot, is the island?
To find the distance from the helicopter to point P, we can use trigonometry.
Let x be the distance from the helicopter to point P. We can use the tangent function, which is defined as the opposite side (1250 feet) divided by the adjacent side (x).
tan(47 degrees) = 1250 / x
Now, we can solve for x:
x = 1250 / tan(47 degrees)
x ≈ 1023.60 feet
Therefore, the island is approximately 1023 feet away from the coast.