Applications of Trigonometric Functions

Question

A helicopter hovers 950 feet above a small island.

The figure shows that the angle of depression from the helicopter to point P on the coast is 35 degrees. How far off the coast, to the nearest foot, is the island?

Answer 1

The height of the helicopter is 950 feet. The angle of depressions is 35 degrees. We seek the adjacent side and the height is the opposite side. So,

tan(35) = opposite / adjacent = 950 / x

x = 950 / tan(35) = 1,357 feet.

ADJACENT HELICOPTER

_________________

| O * / | * 35 DEGREE ANGLE

| P / |

| P / |

| O / |

| S / |

| I / | 950 FEET DOWN

| T / |

| E / |

| / |

| / |

| / |

COAST ISLAND

Answer 2

If the angle of depression from the horizontal is 35°, then the angle with respect to the horizontal is:

90° – 35° = 55°

The helicopter's vertical height is 950 ft, so we can use a trigonometric function (tangent) to find the horizontal distance to the island:

tan(55º) = x / 950 ft

950 ft tan(55)° = x

1,357 ft = x