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?

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) (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 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , ,

Square to get .

Square to get .

Subtract from both sides.

Combine like terms.

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

Simplify the square root.

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Answer:

So the solution is which approximates to .

So the exact length is units while the approximate length is units.
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