SOLUTION: A plane flying at a height of 3.5 miles is at point C. At that point the angle of depression to city A is measured to be 48 degrees and the agnle of depression to city B is measure

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Question 438302: A plane flying at a height of 3.5 miles is at point C. At that point the angle of depression to city A is measured to be 48 degrees and the agnle of depression to city B is measured to be 36 degrees. Calculate the distance in miles between cities A and B.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
The angle of depression is the angle below the horizontal from the plane to
each of the cities. This angle is also equal to the angle from the horizontal
up to the plane from the cities. The tangent of this angle will be equal to
the height of the plane divided by the distance from the city to the point C along the ground
Let a = the distance from city A to point C
Let b = the distance from city B to point C
For city A we have
tan(48) = 3.5/a
And for city B we have
tan(36) = 3.5/b
Solve for a and b:
a = 3.5/tan(48) = 3.151 miles
b = 3.5/tan(36) = 4.817 miles
Therefore the distance from city A to city B is:
3.151 + 4.817 = 7.968 miles