Question

2. The Geo Air pilot is looking at SCCA from the plane. From the aircraft the angle of depression is 17 degrees. If the plane is at an altitude of 10,000 feet, approximately how far is the plane to SCCA? Round your answer to the nearest tenth. The image is not drawn to scale. (2 points)

Answer 1

The distance from the plane to SCCA is 34,203.0 feet approximately, and the horizontal distance is 32,708.5 feet approximately.

Explanation:

You can draw a right triangle like the one shown in the figure attached, where:

x: horizontal distance.

y: distance from the plane to SCCA.

You can calculate x as following:

`tan\alpha=(opposit)/(adjacent)`

Where:

`\alpha=17\°\\opposite=10,000\\adjacent=x`

Substitute and solve for x:

`tan(17\°)=(10,000)/(x)\\\\x=(10,000)/(tan(17\°))\\\\x=32,708.5ft`

You can calculate y as following:

`sin\alpha=(opposit)/(hypotenuse)`

Where:

`\alpha=17\°\\opposite=10,000\\hypotenuse=y`

Substitute and solve for y:

`sin(17\°)=(10,000)/(y)\\\\y=(10,000)/(sin(17\°))\\\\y=34,203.0ft`