Question 438302
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