SOLUTION: A guy wire of length 50 feet is attached to the ground and the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to t

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Question 151848:
A guy wire of length 50 feet is attached to the ground and the top of an antenna. The height of the antenna is 10 feet larger than the distance from the base of the antenna to the point where the guy wire is attached to the ground. What is the height of the antenna?

x-2 from the ladder to the house
10ft from the ground to the top of the house
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
LADDER=X+10
DISTANCE FROM BASE OF LADDER & WIRE=X.
(X+10)^2+X^2=50^2
X^2+20X+100+X^2=2500
2X^2+20X+100-2500=0
2X^2+20X-2400=0
2(X^2+10X-1200)=0
2(X+40)(X-30)=0
X-30=0
X=30FT. FOR THE DISTANCE FROM THE BOTTOMM OF THE ANTENNA TO THE WIRE.
30=10=40FT. IS THE HEIGHT OF THE ANTENNA.
PROOF:
30^2+40^2=50^2
900+1600=2500
2500=2500