a] Using sine rule: a/sin A=c/sin C thus we can rewrite this as: a/c=sin A/sinC given that the ratio of a:c=2:√3+1 and C=60 thus 2/(√3+1)=sin A/sin 60 sin A=(2sin 60)/(√3+1) sin A=0.63398 A=arcsin 0.63398~39.35°
b] In triangle ABC, a = 3, b = 5, and c = 7. Find the measure of B. the value of B will be found using cosine rule as follows: b²=a²+c²+2acCosB thus 5²=3²+7²-2×3×7cos B thus 25=9+49-42cos B -33=-42cosB cosB=0.7857 B=arccos 0.7857 B=38.21°
