SOLUTION: For safety reasons, the base of a 26 foot ladder should be at least 8 feet from the wall.How high can a 26 foot ladder safely reach?

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Question 117600: For safety reasons, the base of a 26 foot ladder should be at least 8 feet from the wall.How high can a 26 foot ladder safely reach?
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%2Cx%29%2C%0D%0Alocate%281%2C-0.2%2C8%29%2C%0D%0Alocate%281%2C2%2C26%29%0D%0A%29
Since we can see that the triangle has legs of x and 8 with a hypotenuse of 26, 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



x%5E2%2B8%5E2=26%5E2 Plug in a=x, b=8, and c=26. Now lets solve for x


+x++%5E+2+%2B+6+4+=+6+7+6 Square each individual term



+x++%5E+2+=+6+7+6+-+6+4 Subtract 64 from both sides


+x++%5E+2+=+6+1+2 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+6+1+2+%29 Take the square root of both sides



x=6%2Asqrt%2817%29 Simplify the square root

Which approximates to...
x+=+2+4+.+7+3+8+6+3+3+7+5+3+7+0+6

So our answer is
x+=+2+4+.+7+3+8+6+3+3+7+5+3+7+0+6


So the ladder can reach about 24.74 feet