<span>The problem is to calculate the angles of the triangle. However, it is not clear which angle you have to calculate, so we are going to calculate all of them </span> we know that Applying the law of cosines c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b] a=12.5 b=15 c=11 so cos C=[a²+b²-c²]/[2*a*b]---> cos C=[12.5²+15²-11²]/[2*12.5*15] cos C=0.694------------> C=arc cos (0.694)-----> C=46.05°-----> C=46.1°
applying the law of sines calculate angle B 15 sin B=11/sin 46.1-----> 15*sin 46.1=11*sin B----> sin B=15*sin 46.1/11 sin B=15*sin 46.1/11-----> sin B=0.9826----> B=arc sin (0.9826) B=79.3°
calculate angle A A+B+C=180------> A=180-B-C-----> A=180-79.3-46.1----> A=54.6°
the angles of the triangle are A=54.6° B=79.3° C=46.1°
