We need the Law of Cosines: .In what ratio are the sides of a triangle if one of the angles is 120°
and the sides of the triangle make up a arethmetic sequence?
so we have 3 sides: a = a, b = a +d , c = a +2d . . . . Good!
and one of the angles is 120° = angle between a and a+d (the shortest sides). . Right!
So we have: .
Since , we have: .
. . which simplifies to: .
And we get: .
The shortest side is: .
The next side is: .
The longest side is: .
The ratio of the sides is: .
. . Multiply by
Therefore, the ratio of the sides is: .