Indeed the solution I get is $\;57.215^\circ\;$ . You have the right formula but maybe you messed between the sides. It should be
$$\cos\alpha=\frac{5^2+7.4^2-6.3^2}{74}$$
Indeed the solution I get is $\;57.215^\circ\;$ . You have the right formula but maybe you messed between the sides. It should be
$$\cos\alpha=\frac{5^2+7.4^2-6.3^2}{74}$$