1. ## Problem Solving

Working from his instruments, a pilot flying at an altitude of 1300 m just above a thick cloudbank decides that his angle of descent to the airport 12km away will be 6.2 degrees. If the cloudbank is 350m thick, how far from the airport will the plane be when it comes out of the cloudbank into clear sky?

2. Originally Posted by Mr Rayon
Working from his instruments, a pilot flying at an altitude of 1300 m just above a thick cloudbank decides that his angle of descent to the airport 12km away will be 6.2 degrees. If the cloudbank is 350m thick, how far from the airport will the plane be when it comes out of the cloudbank into clear sky?
Draw the figure.
It is a big right triangle whose vertical leg is 1300m, and whose horizontal leg is 12,000m.
Then in that, draw a horizontal line segment that is 350m from the top.
Then, at the intersection of the above line segment with the hypotenuse of the big right triangle, drop a vertical line segment to the horizontal leg of the big right triangle. A smaller right triangle is formed here whose vertical leg is (1300 -350) = 950m and whose horizontal leg is , say, x meters.
This x is what you are looking for.

The big right triangle and the said smaller right triangle are similar, hence proportional.
By proportion,
(vertical leg)/(horizontal leg) of big right triangle = (vertical leg)/(horizontal leg) of smaller right triangle
1300/12,000 = 950/x
Cross multiply,
1300*x = 12,000*950
x = 12,000*950 /1300 = 8769m ----------answer.