Solve the following triangles Be sure to give all possible t

Solve the following triangles. Be sure to give all possible triangles. In the ambiguous case, make sure you at least check for two triangles, if applicable. Round final answers to the nearest tenth.

(a)      A=55°, a=40, b=120

(b)         A=35°, a=3, c=4

Solution

a. Using sine law

sinA/a=sinB/b

sin 55/40=sinB/120

Sin B=120 sin 55/40=2.46

No triangle possible

b. sin 35/3=sinB/4

sinB=4 sin 35/3

B₁=49.89 degree

B₂=180-49.89=130.11 degree

C₁=180-A-B₁=95.11

C₂=180-A-B₂=14.89 degree

sinA/a=sinC₁/c₁Sin 35/3=sin95.11/c₁

c₁=5.21

sin A/a=sinC₂/c₂

sin 35/3=sin14.89/c₂

c₂=1.34