Question

The angle of depression from an airplane to the top of an air traffic
control tower is 56 degrees. If the tower is 320 feet tall and the airplane
is flying at an altitude of 7,450 feet, how far away is the airplane from the
control tower?

Answer 1

Answer: approximately 8600.33397283284 feet

Round this however you need to.

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Work Shown:

Check out the diagram below. We have the following points

• A = base of the tower
• B = point on the ground directly below the airplane
• C = top of the tower
• D = plane's location
• E = point used to form the angle of depression

Based on those points, we know that

• AC = 320 = height of tower
• BD = 7450 = height of plane
• CE = BD - AC = 7450-320 = 7130 = difference between the two heights

Which allows us to find the distance from C to D. Focus solely on triangle EDC. Use the sine ratio to find x.

sin(angle) = opposite/hypotenuse

sin(angle EDC) = CE/CD

sin(56) = 7130/x

x*sin(56) = 7130

x = 7130/sin(56)

x = 8600.33397283284 approximately

Make sure your calculator is in degree mode.