Question

> In the following triangle, find the values of the angles B and B'. Which are the best approximations to the solutions?

Answer 1

Answer:

Step-by-step explanation:

apply sine rule 2 the triangle on left:

sinB'/10=sin45deg/8.2

sinB'=10*sin45deg/8.2=0.8623

B'=59.58deg or 120.42deg

as shown in the pic, B' > 90deg.

so B'=120.42deg.

the triangle on right has 2 sides at 8.2 so it is isosceles

B=adjacent < of B'

=180-120.42

=59.58deg

Answer 2

Answer:

B=59.58

B'=120.42

Step-by-step explanation:

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