A helicopter hovers 850 feet above a small island. The figure shows that the angle of depression from the helicopter to point P is
41°. How far off the coast, to the nearest tenth of a foot, is the island?
Write the equation, and show all your work to solve for the indicated length.
Let "x" be the distance from the helicopter to the coast of the island.
According to the problem, the helicopter is 850 feet above the island, and the angle of depression from the helicopter to point P is 41 degrees.
By using trigonometry, we can set up the equation:
tan(41°) = x / 850
To find "x", we multiply both sides of the equation by 850:
850 * tan(41°) = x
Using a calculator, we can find the value of tan(41°) to be approximately 0.8691.
Therefore,
850 * 0.8691 = x
x ≈ 738.7
So, the distance from the helicopter to the coast of the island is approximately 738.7 feet.