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When using the Pythagorean theorem with a triangle, how do you know which numbers, and x, go where in the theorem?

For example, if I have a right trianle with the sides of $150$, $170$ and $x$, where $170$ is the hypotenuse, how do I know where to put the numbers in the theorem? Is it $150^2 + 170^2 = x^2$ or $150^2 + x^2 = 170^2$ or $170^2 + x^2 = 150^2$?

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  • $\begingroup$ By reading the problem statement carefully, drawing a sketch of a right triangle, and labeling its sides. $\endgroup$ – user147263 Mar 6 '15 at 3:12
  • $\begingroup$ I mean I have a right trianle with the sides of 150, 170 and x, 170 is the hypotenuse, how do I know where to put the numbers in the theroem. Ex. is it 150^2 + 170^2 = x^2? or 150^2 + x^2 = 170^2 or 170^2 + x^2 = 150^2? $\endgroup$ – guest1 Mar 6 '15 at 3:15
  • $\begingroup$ For a right triangle,the square of the hypotenuse is always greater than the sum of the squares of the adjacent sides. $\endgroup$ – Mark Viola Mar 6 '15 at 3:34
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The theorem says $$\text{(one leg)}^2+\text{(another leg)}^2 = \text{(hypotenuse)}^2$$ In which order you put the two legs does not matter; the result of addition does not depend on the order of terms. But you need to pay attention to which side is the hypotenuse.

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