An airplane is 3800 feet above the ground. The angle of depression between the airplane and the airport is 8.5°. How far does the plane have to fly in order to land and what is the plane's ground distance to the airport?

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Since angle of depression equals angle of elevation, the angle of elevation from the airport is also 8.5˚.  To find how far to the airport, we want to find the hypotenuse of the right triangle (See image).  To find this we can use the sine ratio.  

`sin/_ = (opp)/(hyp)`

`sin 8.5 = 3800 / x`

`x = 3800 / (sin 8.5)` ≈ ` 25708.782``feet`

The ground distance can be found by using the tangent ratio.

`tan/_ = (opp)/(adj)`

`tan 8.5˚ = 3800 / y`

`y = 3800 / (tan 8.5)` ≈ `25426.394 feet`

The plane has to fly 25,708.782 feet in order to land and the plane's ground distance to the airport is 25,426.394 feet.

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