SOLUTION: In a right triangle, find the length of the side not given. Given an exact answer and an approximate to three decimal places. Assume C represent the length of the hypotenuse 6 & 8

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Question 549819: In a right triangle, find the length of the side not given. Given an exact answer and an approximate to three decimal places. Assume C represent the length of the hypotenuse 6 & 8 = C
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you have a triangle with legs of length 6 and 8.


We basically have this triangle set up:





To find the unknown length, we need to use the Pythagorean Theorem.


Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are 6 and 8 this means that a=6 and b=8


Also, since the hypotenuse is x, this means that c=x.


a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


6%5E2%2B8%5E2=x%5E2 Plug in a=6, b=8, c=x


36%2B8%5E2=x%5E2 Square 6 to get 36.


36%2B64=x%5E2 Square 8 to get 64.


100=x%5E2 Combine like terms.


x%5E2=100 Rearrange the equation.


x=sqrt%28100%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


x=10 Simplify the square root.


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Answer:


So the solution is x=10.


So the missing side is 10 units long.