Solve the SSA triangle Indicate whether the given measuremen

Solve the SSA triangle. Indicate whether the given measurements result in no triangle, one triagle or two triangles. Solve each resulting triangle. Round each answer to the nearest tenth.

B=45degrees b=31 c=40

Select the correct choice.

A) There are two possible solutions.

The measurements for the solution with the longer side a are as follows. A1=___degrees? C1=___degrees? a1=___?

The measurements for the solution with the shorter side a are as follows. A2=___degrees? C2=___degrees? a2=___?

B) There is only one possible solution.

The measurements for the remaining angles A and C and side a are as follows. A=___degrees? C=____degrees? a=___? (Round to nearest tenth as needed)

C) There are no possible solutions.

Solution

B=45 , b=31, c=40

sinB/b=sinC/c

sin 45/31=sinC/40

C₁=65.4 degree

C₂=180-C₁=114.6 degree

A₁=180-B-C₁=69.6 degree

A₂=180-B-C₂=20.4 degree

sinB/b=sinA₁/a₁

sin45/31=sin69.6/a₁

a₁=41.1

sin 45/31=sin20.4/a₂

a₂=15.3