Two sides and an angle SSA of a triangle are given Determine

Two sides and an angle (SSA) of a triangle are given. Determine whether the given measurements produce one triangle, two triangle, or no triangle B = 41 degree, a = 4, b = 3 no triangle A = 29 degree C = 110 degree, c = 5.7

Solution

B=41^o,a=4,b=3

by law of sines

a/sinA = b/sinB

4/sinA=3/sin41^o

sinA=(4/3)sin41^o

A=61^o,119^o

2 triangles possible

i)A=61^o,B=41^o

C=180-61-41=78^o

a/sinA = c/sinC

4/sin61 = c/sin78

c=4.5

i)A=119^o,B=41^o

C=180-119-41=20^o

a/sinA = c/sinC

4/sin119= c/sin20

c=1.6