Explanation:
law of sine :
a/sin(A) = b/sin(B) = c/sin(C)
extended Pythagoras :
c² = a² + b² - 2×a×b×cos(C)
and : the sum of all angles in a triangle is always 180°.
1.
b² = 42.1² + 37² - 2×42.1×37×cos(13) =
= 105.8575002...
b = 10.28870741...
b/sin(13) = 37/sin(C)
sin(C) = 37 × sin(13)/b = 0.808963525...
C = 53.99478824...° ≈ 54°
A = 180 - 13 - 54 ≈ 113°
2.
c² = 18² + 13² - 2×18×13×cos(115) = 690.7853465...
c = 26.28279564...
c/sin(115) = 18/sin(A)
sin(A) = 18 × sin(115)/c = 0.62069273...
A = 38.36673893...°
B = 180 - 115 - A = 26.63326107...°
3.
the length of b is missing.
this cannot be solved without the missing information