Question

In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C.

Answer 1

$$\begin{gathered} \mathrm{GIven}:a=18,b=24\text{and}c=30. \\ \cos A=\frac{b^2+c^2-a^2}{2bc}=\frac{576+900-324}{2\times 24\times 30}=\frac{1152}{1140}=\frac{4}{5} \\ \cos B=\frac{a^2+c^2-b^2}{2ac}=\frac{324+900-576}{2\times 18\times 30}={\displaystyle \frac{648}{1080}}=\frac{3}{5} \\ \cos C=\frac{a^2+b^2-c^2}{2ab}=\frac{576+324-900}{2\times 24\times 18}=0 \end{gathered}$$

Hence, $\cos A=\frac{4}{5},\cos B=\frac{3}{5},\cos C=0$