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

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Question 45575: Towering Antenna. A guy wire of length 50 ft. is attached to the ground and to the top of an antenna. The height of the antenna is 10 ft. 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? Please show all work steps and solution. Thanks
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A guy wire of length 50 ft. is attached to the ground and to the top of an antenna. The height of the antenna is 10 ft. 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?
Draw the picture.
The guy wire is the hypotenuse of a right triangle.
The ground distance is the base of the triangle---let its length be "x".
The height of the tower is the 3rd side of the triangle--height = "x+10".
EQUATION:
Use Pythagoras to get:
x^2 + (x+10)^2 = 50^2
x^2 + x^2 +20x +100 = 2500
2x^2+20x-2400=0
x^2+10x-1200=0
(x+40)(x-30)=0
x=30 ft
x+10=40 ft (the height of the antenna)
Cheers,
Stan H.