Answer
A=$41^{\circ}$
B=$61^{\circ}$
C=$78^{\circ}$
Work Step by Step
Given information :
a=42.1 m
b=56.8m
c=63.4m
Now apply the cosine rule
cos A=$\frac{b^{2}+ c^{2} + a^{2}}{2bc}$
cos A=$\frac{56.8^{2}+ 63.4^{2} + 42.1^{2}}{2\times56.8\times63.4}$
=0.76
A=$cos^{-1} 0.76$
=$41^{\circ}$
Now apply the cosine rule
cos B=$\frac{a^{2}+ c^{2} - b^{2}}{2ac}$
cos B=$\frac{42.1^{2}+ 63.4^{2} + 56.8^{2}}{2\times42.1\times63.4}$
=0.48
B=$cos^{-1} 0.48$
=$61^{\circ}$
C=$180^{\circ} -(A+B)$
C=$180^{\circ} -(41+61)$
=$78^{\circ}$
