# 10.2 The Cosine Rule

10.2 The Cosine Rule

The cosine rule can be used when
(i) two sides and the included angle, or
(ii) three sides of a triangle are given.

(A) If you know 2 sides and 1 angle between them [included angle] Þ Cosine rule

Example:

Calculate the length of AC, x, in cm for the triangle above.
Solution:

(B) If you know 3 sides Þ Cosine rule

Example:

Calculate ÐBAC for the triangle above.
Solution:
$\begin{array}{l}\mathrm{cos}A=\frac{{b}^{2}+{c}^{2}-{a}^{2}}{2bc}\\ \mathrm{cos}\angle BAC=\frac{{7}^{2}+{6}^{2}-{8}^{2}}{2\left(7\right)\left(6\right)}\\ \mathrm{cos}\angle BAC=0.25\\ \angle BAC={\mathrm{cos}}^{-1}0.25\\ \angle BAC={75.52}^{o}\end{array}$