Question 932322
a=38, c=44, ∠A = 35° 
What I have so far: 
sin(35)/38 = sinC/44 
44sin(35) = 38sinC 
44sin(35)/38 = sinC 
sinC = 0.6641 
sin^-1(0.6641) 
∠C = 41.6º 
Is this ∠C1?
Comment:: yes
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B = 180-(35+41.6) = 103.39 degrees
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c/sin(C) = b/sin(B)
44/0.6641 = b/0.97
b = 0.97*44/0.6641
b = 64.45
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Cheers,
Stan H.
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After this I don't know how to derive the rest.
Comment:: After you have A and B, subtract their sum from 180 to get C
Use the Law of Sines to find side "c".
 
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For the second problem: 
a = 76, b = 105, ∠A = 29° 
sin(29)/76 = sinB/105 
105sin(29) = 76sinB 
sinB = 105sin(29)/76 
sin^-1(0.6698) 
∠B = 42.1º