How do you classify the triangle given 2 yd, 3 yd, 4 yd?

Question

2971 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-14T20:27:00

This is an obtuse scalene triangle.

Let #a = 2#, #b = 3# and #c = 4# be the lengths of the sides.

The angle #gamma# opposite the side of length #c# satisfies the law of cosines:

#c^2=a^2+b^2-2ab cos(gamma)#

So:

#gamma = arccos((a^2+b^2-c^2)/(2ab))#

#=arccos((4+9-16) / 12)#

#=arccos(-1/4) > pi/2#

So the triangle is obtuse.

It is scalene since all the sides are of different lengths.