Answer:
[tex]m\angle A\approx112.72^\circ[/tex]
Step-by-step explanation:
Since only side lengths are given and no angles, we are forced to use the Law of Cosines. The equation to find angle A is [tex]\displaystyle \cos(A)=\frac{b^2+c^2-a^2}{2bc}[/tex]:
[tex]\displaystyle \cos(A)=\frac{b^2+c^2-a^2}{2bc}\\\\\cos(A)=\frac{10.1^2+24.3^2-29.7^2}{2(10.1)(24.3)}\\\\A=\cos^{-1}\biggr(\frac{10.1^2+24.3^2-29.7^2}{2(10.1)(24.3)}\biggr)\\\\A\approx112.72^\circ[/tex]
