Use the Law of Sines to solve for all possible triangles tha

Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that A_1 is smaller than A_1.) a = 28, c = 18, C = 21 degree A_1 = A_2 = B_1 = B_2 = b_1 = b_2 =

Solution

given a= 28,c=18,C=21^o

by law of sines

a/sinA=c/sinC

28/sinA=18/sin21^o

sinA=(28/18)sin21^o

sinA=0.55746

A₁=33.9^o,A₂=146.1^o

A₁+B₁+C=180^o

33.9^o+B₁+21^o=180^o

B₁=125.1^o

A₂+B₂+C=180^o

146.1^o+B₂+21^o=180^o

B₂=12.9^o

b₁/sinB₁=c/sinC

b₁/sin125.1^o=18/sin21^o

b₁=18sin125.1^o/sin21^o

b₁=41.1

b₂/sinB₂=c/sinC

b₂/sin12.9^o=18/sin21^o

b₂=18sin12.9^o/sin21^o

b₂=11.2