A helicopter hovers 650 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is 31 degrees. How far is the distance from the helicopter to the point P, the hypotenuse of the triangle formed, to the nearest foot.
To find the distance from the helicopter to point P, we can use trigonometry.
We can see that the angle of depression of 31 degrees forms a right triangle with the horizontal line from the helicopter to point P. The helicopter is 650 feet above the island, which is the opposite side of the triangle, and we are looking for the hypotenuse.
Using the tangent function:
tan(31 degrees) = opposite/adjacent
tan(31 degrees) = 650/x
Multiplying both sides by x:
x * tan(31 degrees) = 650
Dividing by tan(31 degrees):
x = 650 / tan(31 degrees)
x ≈ 1144 feet
Therefore, the distance from the helicopter to point P is approximately 1144 feet.