Question

A plane is 100,000 feet from the airpoirt when it begins its descent at an angle of

depression of 20°. At the same time a car is directly underneath the plane on the
ground. How many feet from the airport is the car? Round to nearest foot. (No
decimals).

Answer 1

`\large\boxed{93,969feet}`

Step-by-step explanation:

1. The plane, the airport and the car directly underneath the plane on the ground form a right triangle.

2. The distance of 100,000 feet from the plane to the airport is represented by the hypotenuse of the triangle.

3. The 20º angle of depression is related with the hypotenuse and the distance from the car to the airport by the cosine ratio.

Naming
`x` the distance from the car to the airport the cosine ratio is:

`cos(20\textdegree)=(adyacent-leg)/(hypotenuse)\\ \\ cos(20\textdegree)=x/100,000`

Clearing
`x`, you get:

`x=100,000cos(20\textdegree)\\ \\ x=93,969`

The units were omitted in the equation but they are feet, so the answer is:

`\large\boxed{93,969feet}`