State whether a triangle formed with sides having the lengths named is acute, right, or obtuse.
3,4,6
9,12,15
5,6,7
How the heck can I solve this? Please explain!
Use the law of cosines or Heron's formula.
Let us use law of cosines, because you have a better chance of hearing of it.
#1] Let a=3 b=4 and c=6.
Then, we can find all the angles of this triangle.
Say angle A.
a^2=b^2+c^2-2bc*cos(A)
9=16+36-48*cos(A)
You can solve for cos(A) and then take arccos to get the angle.
Now do that will all angles.
Then you can determine whether the triangle if acute or not.