To find the value of C we need to use the sine rule.

This means that we need to find the value of the side opposite angleC and one other side and opposite angle.

5.5sin(C)=5.5sin(73.63°)

Next we multiply both sides by sin(C):

5.5=sin(C)×5.5sin(73.63°)

Multiply both sides by sin(73.63°):

5.5×sin(73.63°)=sin(C)×5.5

Divide both sides by 5.5:

5.5×sin(73.63°)5.5=sin(C)

Swap the sides around and take the inverse sin of both sides: 

sin(C)=5.5×sin(73.63°)5.5

C=sin−1(5.5×sin(73.63°)5.5)=73.63°