SOLUTION: what type of triangle is a triangle with the sides lengths of 37,12 and 34? thank you!

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Question 862732: what type of triangle is a triangle with the sides lengths of 37,12 and 34?
thank you!
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Check first for a fit to Pythagorean Theorem relationship.
37%5E2 versus 12%5E2%2B34%5E2
1369 versus 1300 are not equal.

Maybe not the best way, but workable:
a%5E2%2Bb%5E2-2ab%2Acos%28s%29=c%5E2
-2ab%2Acos%28s%29=c%5E2-a%5E2-b%5E2
highlight_green%28cos%28s%29=%28a%5E2%2Bb%5E2-c%5E2%29%2F%282ab%29%29
Is the angle opposite the 37 greater than 90 degrees? c=37.
cos%28s%29=%2812%5E2%2B34%5E2-37%5E2%29%2F%282%2A12%2A34%29
cos%28s%29=%28-69%29%2F%28816%29
Obviously a small negative number, so s is in quadrant number 2, meaning s is like 90%3Cs%3C180 using degrees measure. Angle s is obtuse.

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ANSWER: OBTUSE TRIANGLE.
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