SOLUTION: Two vertical poles on the football field are 20 and 30 meters high. Wires are connected from the top of each pole to the bottom of the other. If the field is perfectly level, and t

Question 729239: Two vertical poles on the football field are 20 and 30 meters high. Wires are connected from the top of each pole to the bottom of the other. If the field is perfectly level, and the poles are 50 meters apart, how far above the ground do the two wires cross?

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let AP = 20 m
Let BQ = 30 m
AQ is one rope
BP is the other rope
They intersect at M
WE have to find MT
In triangle APQ
Tan AQP = 20/50 = 2/5
Tan BPQ = 3/5
Let PT be y
QT = 50-y
Let MT =x
Tan MQT = x/(50-y) = 2/5
5x=2(50-y)
5x+2y=100.......................(1)
Tan MPT= x/y= 3/5
5x-3y=0.......................(2)

solve equations (1) & (2)
5.00 x + 2.00 y = 100.00 .............1
Total value
5.00 x -3.00 y = 0.00 .............2
Eliminate y
multiply (1)by 3.00
Multiply (2) by 2.00
15.00 x 6.00 y = 300.00
10.00 x -6.00 y = 0.00
Add the two equations
25.00 x = 300.00
/ 25.00
x = 12m

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