SOLUTION: A 25-foot ladder leaning against a building touches the wall 16 feet above the ground. How far from the building is the bottom of the ladder?

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Question 88645: A 25-foot ladder leaning against a building touches the wall 16 feet above the ground. How far from the building is the bottom of the ladder?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:



Since we can see that the triangle has legs of 16 and x with a hypotenuse of 25, 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



16%5E2%2Bx%5E2=25%5E2 Plug in a=16, b=x, and c=25. Now lets solve for x


2+5+6+%2B++x++%5E+2+=+6+2+5 Square each individual term



+x++%5E+2+=+6+2+5+-+2+5+6 Subtract 256 from both sides


+x++%5E+2+=+3+6+9 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+3+6+9+%29 Take the square root of both sides


x=3%2Asqrt%2841%29 Simplify the square root


Which approximates to...
x+=+1+9+.+2+0+9+3+7+2+7+1+2+2+9+8+5

So our answer is
x+=+1+9+.+2+0+9+3+7+2+7+1+2+2+9+8+5


So the bottom of the ladder is about 19.21 feet from the building