SOLUTION: A wire is stretched from the ground to the top of an antenna tower. The wire is 20 ft long. The height of the tower is 4ft greater than the distance from the towers base to the bot

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Question 279652: A wire is stretched from the ground to the top of an antenna tower. The wire is 20 ft long. The height of the tower is 4ft greater than the distance from the towers base to the bottom of the wire. Find the distance and the height of the tower. Please assist!!!!
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
the hypotenuse is the length of the wire.
20^2=(x+4)^2+x^2
400=x^2+8x+16+x^2
400=2x^2+8x+16
200=x^2+4x+8
0=x^2+4x-192
(x-12)*(x+16)=0
x=12 distance from base to wire
x+4=16 height of tower
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-192+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A1%2A-192=784.

Discriminant d=784 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+784+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+784+%29%29%2F2%5C1+=+12
x%5B2%5D+=+%28-%284%29-sqrt%28+784+%29%29%2F2%5C1+=+-16

Quadratic expression 1x%5E2%2B4x%2B-192 can be factored:
1x%5E2%2B4x%2B-192+=+1%28x-12%29%2A%28x--16%29
Again, the answer is: 12, -16. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-192+%29