SOLUTION: Find the missing side of the triangle. Give your answer as a simplified radical. "5^2+b^2=10^2"

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Question 84072: Find the missing side of the triangle. Give your answer as a simplified radical.
"5^2+b^2=10^2"
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since we have a triangle with legs of 5 , x(our unknown side) and a hypotenuse of 10, we can use Pythagoreans theorem to find the unknown side.
Pythagoreans theorem
a%5E2%2Bb%5E2=c%5E2

5%5E2%2Bb%5E2=10%5E2 Plug in a=5 and c=10 and lets solve for b
2+5+%2B++b++%5E+2+=+1+0+0 Square each individual term



+b++%5E+2+=+1+0+0+-+2+5 Subtract 25 from both sides


+b++%5E+2+=+7+5 Combine like terms


s+q+r+t+%28++b++%5E+2+%29+=+s+q+r+t+%28+7+5+%29 Take the square root of both sides


b+=+s+q+r+t+%28+7+5+%29 Simplify


b=sqrt%2825%2A3%29 Factor 75 into 25*3

b=sqrt%2825%29%2Asqrt%283%29 Break up the square roots using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

b=5%2Asqrt%283%29 Take the square root of the perfect square 25 to get 5

So our answer is
b=5%2Asqrt%283%29