What Is the Law of Sines and Cosines?

What Is the Law of Sines and Cosines?

The law of sines and law of cosines are two different equations relating the measure of the angles of a triangle to the length of the sides. The laws apply to any triangle, not just right-angled triangles.

Draw a triangle. Label the angles A, B and C and the opposite sides a, b and c. The law of sines says that the sines of the angles are proportional to the lengths of the opposite sides. That means sin A/a = sinB/b = sinC/c.

The law of cosines says that for any triangle, the square of the length of any side equals the sum of the squares of the other two sides minus 2 times the product of those two sides times the cosine of the included angle. If seeking the length of side a, for example, use the formula a^2 = b^2 + c^2 - (2bc cosA), and then take the square root of both sides of the equation.