SOLUTION: A plane is flying at an elevation of 21000 feet. It is within sight of the airport and the pilot finds that the angle of depression to the airport is 24 Find the distance betw

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Question 1029933: A plane is flying at an elevation of 21000 feet.
It is within sight of the airport and the pilot finds that the angle of depression to the airport is 24
Find the distance between the plane and the airport.Find the distance between a point on the ground directly below the plane and the airport
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A plane is flying at an elevation of 21000 feet.
It is within sight of the airport and the pilot finds that the angle of depression to the airport is 24
Find the distance between the plane and the airport.
:
Find the interior angle of the right triangle formed by the plane the airport and a point directly below the plane
90 - 24 = 66 degrees
The distance from the plane to the airport is the hypotenuse (h).
The height of the plane is give as 21000
Use the cosine of 66 degrees to find the distance to the airport
cos(66) = 21000%2Fh
.4067h = 21000
h = 21000/.4067
h = 51630 ft to the airport
:
"Find the distance between a point on the ground directly below the plane and the airport."
The distance (d) is the side opposite 66 degrees
Use the sine of 66 degrees
sin(66) = d%2F51630
d = .9135(51630)
d = 47,166 ft, airport to a point directly below the plane
:
:
We can check this by finding d using the tangent of 66 also
tan(66) = d%2F21000