In order to apply the law of cosines to find the length of the side of a triangle, it is enough to know which of the following?

To apply the law of cosines effectively, you need to know either:

• Two sides and the included angle (often referred to as the SSA case).
• All three sides of the triangle (the SSS case).

Let’s break this down:

The law of cosines states that for any triangle with sides a, b, and c, and the angle C opposite side c, the formula is:

c² = a² + b² – 2ab * cos(C)

This formula allows us to calculate the length of a side if we have the lengths of the other two sides and the measure of the included angle. Alternatively, if we know all three sides, we can rearrange the formula to find the angles of the triangle as well.

Thus, having either:

1. Two sides and the angle between them
2. All three sides of the triangle

is sufficient to use the law of cosines to find the length of a triangle’s side.