In ∆abc, if the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively, what are m < b and m m b = 89.68°, and m c = 37.19°

m b = 53.12°, and m c = 89.68°

m b = 89.68°, and m c = 53.13°

m b = 37.20°, and m c = 53.12°

m b = 53.13°, and m c = 37.19°

Use the law of cosines.
a2+b2−2abcosC=c2

Find the measure of angle C. It is the opposite side of c.
c2−a2−b2−2ab=cosC
cosC=13.62−22.52−182−2(22.5)(18)≈0.797
C=cos−10.797=0.649 rad=37.19∘

angle B:
a2+c2−2accosB=b2
cosB=b2−a2−c2−2ac
B=cos−1b2−a2−c2−2ac=cos−1182−22.52−13.62−2(22.5)(13.6)≈0.927 rad=53.13∘

angle A:
b2+c2−2bccosA=a2
A=89.68∘