SOLUTION: A wire of length 50 feet is attached to the ground and 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 whe

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Question 94632: A wire of length 50 feet is attached to the ground and 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 wire is attached to the ground.What is the height of the antenna?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A wire of length 50 feet is attached to the ground and 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 wire is attached to the ground.What is the height of the antenna?
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Draw the picture: a right triangle with hypotenuse = 50 feet; altitude
= x+10; base = x.
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EQUATION:
Use Pythgoras to get:
x^2 + (x+10)^2 = 50^2
x^2 + x^2+20x+100 = 2500
x^2 + 10x -1200 = 0
(x+40)(x-30) = 0
Positive answer:
x = 30 ft (base length)
x+10 = 40 ft (height of tower)
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Cheers,
Stan H.