Step-by-step explanation:
1)
remember the law of cosine (I call this the generic Pythagoras) :
c² = a² + b² - 2ab×cos(C)
C being the angle opposite of the side c. a and b are the other 2 sides. this works for any grouping of the triangle sides. just always use the opposite angle of the third side for the cosine.
so, adjusting this to our numbers and making :
b² = 4.3² + 12.1² - 2×4.3×12.1×cos(110°) =
= 18.49 + 146.41 - -35.59061611... =
= 200.4906161...
b = 14.1594709... ≈ 14.2
2)
12.1² = 4.3² + b² - 2×4.3×b×cos(C)
146.41 - 18.49 - 200.4906161... = -2×4.3×14.1594709...×cos(C)
-72.57061611.../(-2×4.3×14.1594709...) = cos(C)
0.59595756... = cos(C)
C = 53.41907544... ≈ 53
3)
the same principle as in 2) :
16.5² = 12² + 21.3² - 2×12×21.3×cos(B)
16.5² - 12² - 21.3² = -2×12×21.3×cos(B)
272.25 - 144 - 453.69 = -511.2×cos(B)
-325.44 = -511.2×cos(B)
cos(B) = 325.44/511.2 = 0.636619718...
B = 50.45978027... ≈ 50
