Question Number 186282 by Mingma last updated on 03/Feb/23
Answered by mr W last updated on 03/Feb/23
Commented by mr W last updated on 03/Feb/23
$$\mathrm{cos}\:\left({A}−{B}\right)=\frac{\mathrm{4}^{\mathrm{2}} +{x}^{\mathrm{2}} −\left(\mathrm{5}−{x}\right)^{\mathrm{2}} }{\mathrm{2}×\mathrm{4}×{x}}=\frac{\mathrm{7}}{\mathrm{8}} \\ $$$$\Rightarrow{x}=\mathrm{3} \\ $$$$\mathrm{cos}\:{C}=\frac{\mathrm{4}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} }{\mathrm{2}×\mathrm{4}×\mathrm{2}}=\frac{\mathrm{11}}{\mathrm{16}}\:\checkmark \\ $$