SOLUTION: The base of a ladder is 7 feet away from the wall. The top of the ladder is 7 feet from the floor. Find the length of the ladder to the nearest thousandth.

Algebra ->  Algebra  -> Pythagorean-theorem -> SOLUTION: The base of a ladder is 7 feet away from the wall. The top of the ladder is 7 feet from the floor. Find the length of the ladder to the nearest thousandth.      Log On

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Question 96021: The base of a ladder is 7 feet away from the wall. The top of the ladder is 7 feet from the floor. Find the length of the ladder to the nearest thousandth.
Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:

drawing%28500%2C500%2C-0.5%2C2%2C-0.5%2C3.2%2C%0D%0A%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C2%2C0%29%2C%0D%0Aline%282%2C0%2C0%2C0%29%2C%0D%0Alocate%28-0.2%2C1.5%2C7%29%2C%0D%0Alocate%281%2C-0.2%2C7%29%2C%0D%0Alocate%281%2C2%2Cx%29%0D%0A%29
Since we can see that the triangle has legs of 7 and 7 with a hypotenuse of x, we can use Pythagoreans theorem to find the unknown side.


Pythagoreans theorem:

a%5E2%2Bb%5E2=c%5E2 where a and b are the legs of the triangle and c is the hypotenuse



7%5E2%2B7%5E2=x%5E2 Plug in a=7, b=7, and c=x. Now lets solve for x


4+9+%2B+4+9+=++x++%5E+2 Square each individual term



9+8+=++x++%5E+2 Combine like terms


s+q+r+t+%28+9+8+%29+=+s+q+r+t+%28++x++%5E+2+%29 Take the square root of both sides


7%2Asqrt%282%29=x Simplify the square root


Which approximates to...

9.89949493661167=x

So our answer is
x=9.89949493661167


which is 9.899 feet to the nearest thousandth