missing angles and sides?

Question

given a=2, beta=20, c=5

have to find b, alpha, gamma

please help me step by step so I can follow, thanks

Answer 1

You sure you listed your problem correctly:
side a corresponds with Alpha
b corresponds with Beta
c corresponds with Gamma

you need to use law of cosines
b^2 = a^2 + c^2 – 2ac*cos B.
b^2 = 4 + 25 - 20cos(20)
b^2 = 29-18.7939
b^2 = 10.2061
b = 3.1947

Then you use Law of Sines
SinA/a = SinB/b
SinA = (SinB/b)*a
SinA = .2141
A = 12.3637

SinC/c = SinB/b
SinC/c = (SinB/b)*c
SinC = .5353
C = 32.3639

Answer 2

To 1294:

Sinus is OK but the angle should be

C = 147.636°

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