Question:
In ∆ ABC, if a = 18, b = 24 and c = 30, find cos A, cos B and cos C.
Solution:
GIven : $a=18, b=24$ and $c=30$.
$\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c}=\frac{576+900-324}{2 \times 24 \times 30}=\frac{1152}{1140}=\frac{4}{5}$
$\cos B=\frac{a^{2}+c^{2}-b^{2}}{2 a c}=\frac{324+900-576}{2 \times 18 \times 30}=\frac{648}{1080}=\frac{3}{5}$
$\cos C=\frac{a^{2}+b^{2}-c^{2}}{2 a b}=\frac{576+324-900}{2 \times 24 \times 18}=0$
Hence, $\cos A=\frac{4}{5}, \cos B=\frac{3}{5}, \cos C=0$