Answer
$A =39.52^\circ$
$B =83.85^\circ$
$C =56.63^\circ$
Work Step by Step
$\cos{A} = \dfrac{b^2+c^2-a^2}{2bc} = \dfrac{(75)^2+(63)^2-(48)^2}{2 \times 75 \times 63} = 0.771$
$$\therefore A = \boxed{39.52^\circ}$$
$\cos{B} = \dfrac{a^2+c^2-b^2}{2ac} = \dfrac{(48)^2+(63)^2-(75)^2}{2 \times 48 \times 63} = 0.107$
$$\therefore B = \boxed{83.85^\circ}$$
$$C = 180-(A+B) = 180-(39.52+83.85) = \boxed{56.63^\circ}$$
