A helicopter hovers 850 feet above a small island the figure shows that the anggle of depression from the helicopter to point P is

41 degrees how far off the coast to the nearest tenth of a foot is the island
write the equation and show all your work tosolve for th indicated length

1 answer

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.