Question

In the following triangle, find the values of the angles B and B, which are thebest approximations to the solutions to this ambiguous case?

Answer 1

For the larger triangle, by sin rule, sinB/10=sin45/8.2

sinB=10*sin45/8.2

For the small triangle on the left hand side, by sin rule, sinB'/10=sin45/8.2

sinB'=10*sin45/8.2

So sinB=sinB' but as B'>90, B and B' are supplementary

B=sin^-1(10*sin45/8.2)=sin^-1(0.8623)=59.58

B'=180-B=180-59.58=120.42

So the anwser is C