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anonymous
 5 years ago
state whether a triangle formed with sides having the lengths named is acute, right, or obtuse. 1)3,4,6 2)9,12,15 3)5,6,7
anonymous
 5 years ago
state whether a triangle formed with sides having the lengths named is acute, right, or obtuse. 1)3,4,6 2)9,12,15 3)5,6,7

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xkehaulanix
 5 years ago
Best ResponseYou've already chosen the best response.0I believe for this you'd use the pythagorean theorem...maybe? You take the two smallest sides and square them. So for part A, it'd be this: \[3^{2}+4^{2}=9+16=25\] Then take the largest side and square it to compare to the value found in the first part. So for this, it would be \[6^{2}=36\] Since 25 is smaller than 36, the third size is larger than expected in a right triangle. The larger a size is, the larger the angle opposite of it is, so the triangle in part A is a right triangle. If you repeat it for B, you get equal values by following the same steps. \[9^{2}+12^{2}=225\]\[15^{2}=225\]Since they are equal, this would be a right triangle. Following the same steps in part C, you should end up with this: \[5^{2}+6^{2}=61\]\[7^{2}=49\]Since the side is shorter than predicted for a right triangle, and since the angle shrinks as the length of the side gets smaller, you can expect it to be an acute triangle. ...at least, that's what I think. I haven't done this kind of math in years...

xkehaulanix
 5 years ago
Best ResponseYou've already chosen the best response.0Oops! The triangle in part A is obtuse, my mistake.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks that was helpfull
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