Question

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

Answer 1

I 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...

Answer 2

Oops! The triangle in part A is obtuse, my mistake.

Answer 3

thanks that was helpfull