Sight Elevation

Sight Elevation
A plane is flying at an elevation of 23000 feet.?

It is within sight of the airport and the pilot finds that the angle of depression to the airport is 18 degrees.

A.) Find the distance between the plane and the airport.

B.) Find the distance between a point on the ground directly below the plane and the airport.

Ignoring the curvature of the Earth, here's how you do it.

The angle of depression is the angle between the horizontal line coming directly from the pilot's eyes, and his line of sight directly to the airport. See the pic here: http://www.mathwords.com/a/angle_depression.htm

For part (A), I'm guessing they want the length of that diagonal line (the hypotenuse of the triangle).

We know the altitude of the plane, which is the "opposite" side of the triangle from the angle. Therefore, we will use sin. We want to find H in sin(18degrees)=23,000/H.

Multiply each side by H and divide by sin(18degrees) to get H=23,000/sin(18degrees)

I'm getting approximately H=74429.56 feet.

For B, you just need to find the other side of the triangle, since the distance from the point below the pilot to the airport would be the same as the distance from the pilot to the point directly above the airport.

Now we need to find A for adjacent side: tan(18degrees)=23,000/A
A=23000/tan(18degrees)
A=70786.72 feet

Въздушна пушка Hatsan Mod. AT 44

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