Solve the triangle ABC if the triangle exists B3454 a384 b30

Solve the triangle ABC, if the triangle exists. B=34°54\' a=38.4 b=30.9

Solution

B=34degree54\"=34.9degree

a=38.4 and b=30.9

using sine law

sinB/b=sinA/a

sin 34.9/30.9=sinA/38.4

sinA=38.4sin34.9/30.9

A=45.32 degree

C=180-(A+B)=99.78

SInC/c=Sin B/b

sin99.78/c=sin34.9/30.9

c=30.9sin99.78/sin34.9=53.2