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...

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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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

See image:

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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