SOLUTION: A right triangle has legs of length 2 and 3 inches. Use the Pythagorean theorem to determine the length of the hypotenuse in inches.

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Question 467402: A right triangle has legs of length 2 and 3 inches. Use the Pythagorean theorem to determine the length of the hypotenuse in inches.
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 2 and 3 this means that a=2 and b=3


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


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


2%5E2%2B3%5E2=x%5E2 Plug in a=2, b=3, c=x


4%2B3%5E2=x%5E2 Square 2 to get 4.


4%2B9=x%5E2 Square 3 to get 9.


13=x%5E2 Combine like terms.


x%5E2=13 Rearrange the equation.


x=sqrt%2813%29 Take the square root of both sides. Note: only the positive square root is considered (since a negative length doesn't make sense).


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Answer:


So the solution is x=sqrt%2813%29 which approximates to x=3.606.