petr,
the Pythagoras Theorem (or Pythagorean Theorem) is used for right triangles.
That first method doesn't apply.
Neither does the second method.
If the angle is 143.13 degrees, you will need a third way.
Edit
Assuming you meant to use the given diagram, use the Law of Cosines:
Let the measure of angle C = 143.13 degrees
Let one of a or b = 12
Then let the other of a and b = 15
Solve for c in this equation:
\(\displaystyle c^2 \ = \ a^2 \ + \ b^2 \ - \ 2ab*cosC\)