Question 44208
The sine rule {{{a/sinA=b/sinB=c/sinC}}} can only be used effectively when you know an angle and the length opposite that angle and one other property (length or angle). Since we don't have this infromation, we have to use the cosine rule {{{a^2=b^2+c^2+2bc*cosA}}} 
This gives us a=22.8 to the nearest tenth.
Now we can use the sine rule:
{{{22.78/sin16=13/sinB=10/sinC)}}}
This solves to give {{{B=arcsin(13/22.78)=34.8}}}
All the angles in any triangle add up to 180 degrees.
{{{A+B+C=180}}}
{{{16+34.8+C=180}}}
{{{C=129.2}}}degrees.

I hope this helps
P.S. I am trying to start up my own homework help website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk