SOLUTION: The length of a hypotenuse of a right triangle is 16 and the length of one leg is 11, what is the length of the other leg

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Question 115195: The length of a hypotenuse of a right triangle is 16 and the length of one leg is 11, what is the length of the other leg
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 11 and x with a hypotenuse of 16, 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



11%5E2%2Bx%5E2=16%5E2 Plug in a=11, b=x, and c=16. Now lets solve for x


1+2+1+%2B++x++%5E+2+=+2+5+6 Square each individual term



+x++%5E+2+=+2+5+6+-+1+2+1 Subtract 121 from both sides


+x++%5E+2+=+1+3+5 Combine like terms


s+q+r+t+%28++x++%5E+2+%29+=+s+q+r+t+%28+1+3+5+%29 Take the square root of both sides


x=3%2Asqrt%2815%29 Simplify the square root


Which approximates to...
x+=+1+1+.+6+1+8+9+5+0+0+3+8+6+2+2+3

So our answer is
x+=+1+1+.+6+1+8+9+5+0+0+3+8+6+2+2+3