This formula is used for solving triangles which are not right angled and in which either two angles and any side are given or two sides and the angle opposite one of them are given.

Sine Rule:

Example 1:

Find the remaining angles of ABC in which a= 12.5cm, C= 17.7cm and C= 1160

Cosine Rule

The Cosine rule, just like sine rule is used to solve for the unknowns in a triangle. Cosine rule is especially use to solve triangles with the following dimension.

Solution

By Cosine Rule

X² = a² + b² – 2ab Cos 80

X² = 32 + 22 -2(3)(2) x 0.1736

X² = 13 – 2.0832

X² = 10.9168

X² =

=3.305cm