SOLUTION: Could someone please help me out? I got this far and now am lost..... A rope is stretched from the ground to the top of a tower. The wire is 10 ft. long. The height is 2 ft grea

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Question 204104: Could someone please help me out? I got this far and now am lost.....
A rope is stretched from the ground to the top of a tower. The wire is 10 ft. long. The height is 2 ft greater than the distance from the towers base to the end of the wire. Find the distance &height.
r(r+10)=2
r(r+10)-2=0
(r- )(r+ ) not sure???????
Found 2 solutions by scott8148, solver91311:
Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
the rope/wire is the hypotenuse of a right triangle formed by the rope/wire, the tower, and the base distance

let x="base distance", so x+2="tower height"

by Pythagoras, x^2 + (x+2)^2 = 10^2 ___ x^2 + x^2 + 4x + 4 = 100 ___ x^2 + 2x +2 = 50

x^2 + 2x - 48 = 0 ___ factoring ___ (x+8)(x-6) = 0 ___ so, x = 6 and x+2 = 8

Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You talk about a rope and then a wire. I'm going to go out on a limb and presume that they are the same object.

What you have is a right triangle where the length of the rope, 10 feet, is the hypotenuse. Let represent the distance from the base of the tower to where the rope meets the ground. Then must be the height of the tower.

So we can say:

Thank you, Mr. Pythagoras. So:

Just solve the quadratic and exclude the negative root.

John