SOLUTION: The length of the hypotenuse of a right triangle is 8 centimeters and the length of one side is 2 centimeters. What is the exact length of the third side?

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Question 221417: The length of the hypotenuse of a right triangle is 8 centimeters and the length of one side is 2 centimeters. What is the exact length of the third side?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

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 x and 2 this means that a=x and b=2


Also, since the hypotenuse is 8, this means that c=8.


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


x%5E2%2B2%5E2=8%5E2 Plug in a=x, b=2, c=8


x%5E2%2B4=8%5E2 Square 2 to get 4.


x%5E2%2B4=64 Square 8 to get 64.


x%5E2=64-4 Subtract 4 from both sides.


x%5E2=60 Combine like terms.


x=sqrt%2860%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=2%2Asqrt%2815%29 Simplify the square root.


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Answer:


So the solution is x=2%2Asqrt%2815%29 which approximates to x=7.746.


So the exact length is 2%2Asqrt%2815%29 units while the approximate length is 7.746 units.