SOLUTION: The bottom of a ladder is placed 8 feet from the wall of a house. The wall and the ground form a right angle. if the ladder is 15 feet in length, how far up the wall does it reach(

Algebra ->  Algebra  -> Length-and-distance -> SOLUTION: The bottom of a ladder is placed 8 feet from the wall of a house. The wall and the ground form a right angle. if the ladder is 15 feet in length, how far up the wall does it reach(      Log On

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Question 117736: The bottom of a ladder is placed 8 feet from the wall of a house. The wall and the ground form a right angle. if the ladder is 15 feet in length, how far up the wall does it reach(to the nearest foot)?
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%2C15%29%0D%0A%29
Since we can see that the triangle has legs of x and 8 with a hypotenuse of 15, 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=15%5E2 Plug in a=x, b=8, and c=15. Now lets solve for x


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



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


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


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


Which approximates to...
x+=+1+2+.+6+8+8+5+7+7+5+4+0+4+4+9+5

So our answer is
x+=+1+2+.+6+8+8+5+7+7+5+4+0+4+4+9+5


so the ladder can reach about 13 ft on the wall