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Question 1096817: A pilot in an ultra-light aircraft knows that her plane in landing configuration will glide a horizontal distance of 22 Km from a height of 1900 meters. A TV transmitting tower is located in a direct line with the local runway. If the pilot glides over the tower with 50 meters to spare, and touches down on the runway at a point 7 Km from the base of the tower, how high is the tower? Hint: use similar triangles (however, it is not the only way to solve this problem) (extra bonus points for using Matlab or Excel)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Drawing this helps
The big triangle is 1.9 km vertical and 22 km horizontal.
The smaller triangle is x+0.05 km vertical and 7 km horizontal.
1.9/22=(x+0.05)/7
cross-multiply
13.3=22x+1.1
12.2=22x
x=0.5545 km tower height or 554.5 m
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Can do by trig
the angle made by the glider has a tangent of 1.9/22, which is 0.0864
the arc tan of that is an angle of 4.936 degrees.
Use that to find the height of the tower x. First, the side will be x+50, because the glider is traveling 50 m above the tower. The other side is 7 km
tangent 4.936=(x+0.50)/7
7 * 0.0864=x+0.05
0.6048-0.05=x=0.5548 km or 554.8 m
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7 km is a little less than 1/3 the total distance, and 554.8 m is a little less than 1/3 the total height from 22 km of 633 m.
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