Law of Cosines

Let us study the law of Cosines,
If α, β, and γ are the angles of any (right, acute, or obtuse) triangle, and a, b, and c are the lengths of the three sides opposite α, β, and γ, respectively, then


These three formulas are called the Law of Cosines. Each follows from the distance formula and is illustrated in Figure 1 .

Figure 1

Reference triangle for Law of Cosines.

From the figure,

Thus the coordinates of A are Remember, all three forms of the Law of Cosines are true even if γ is acute. Using the distance formula, In the preceding formula, if γ is 90°, then the cos 90° = 0, yielding the Pythagoras theorem for right triangles. If the orientation of the triangle is changed to have A or B at the origin, then the other two versions of the Law of Cosines can be obtained. Two specific cases are of particular importance. First, use the Law of Cosines to solve a triangle if the length of the three sides is known. Hope the above explanation was helpful.