Question

The pilot of a helicopter sights a fire at an angle of depression of 11°.

The helicopter's altitude is 1700 feet.
To the nearest foot, what is the distance from the helicopter to the fire?
8909 ft
3204 ft
8746 ft
3300 ft

Answer 1

The distance from the helicopter to the fire is 8909 feet.

Explanation:

Refer the attached figure

The pilot of a helicopter sights a fire at an angle of depression of 11° i.e.
`\angle ACB = 11^(\circ)`

The helicopter's altitude is 1700 feet.i.e.AB = 1700 feet

We are supposed to find the distance from the helicopter to the fire i.e. AC

Using trigonometric ratios

`Sin \theta = Perpendicular}{Hypotenuse}\\\\Sin 11^(\circ)=(AB)/(AC)\\\\Sin 11^(\circ)=(1700)/(AC)\\\\AC=(1700)/(Sin 11^(\circ))\\\\AC=(1700)/(0.1908)\\\\AC=8909.85 feet`

Hence the distance from the helicopter to the fire is 8909 feet.