[tex]|AB|=\sqrt{3^2+5^2}=\sqrt{9+25}=\sqrt{34}\\|AC|=\sqrt{4^2+2^2}=\sqrt{16+4}=\sqrt{20}\\|BC|=\sqrt{1^2+7^2}=\sqrt{1+49}=\sqrt{50}\\ \cos \angle A=\frac{\sqrt{34}^2+\sqrt{20}^2-\sqrt{50}^2}{2\sqrt{34}\sqrt{20}}=\frac{34+20-50}{4\sqrt{170}}=\frac{\sqrt{170}}{170}\\\cos \angle B=\frac{\sqrt{34}^2+\sqrt{50}^2-\sqrt{20}^2}{2\sqrt{34}\sqrt{50}}=\frac{34+50-20}{20\sqrt{17}}=\frac{16\sqrt{17}}{85}\\[/tex][tex]\cos \angle C=\frac{\sqrt{20}^2+\sqrt{50}^2-\sqrt{34}^2}{2\sqrt{20}\sqrt{50}}=\frac{20+50-34}{20\sqrt{10}}=\frac{9\sqrt{10}}{50}[/tex]