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Answer to Question #1203 in Trigonometry for Ali

Question #1203
Question:
Solve ∆ABC, if a=29.3°, b=20.5cm, and a=12.8cm. round the side length to nearest tenth of centimeter angles degree, if necessary. include all solutions.
Expert's answer
According to the law of cosines:
c2 = a2 + b2 - 2ab cos (∠ a) =12.82 + 20.52 - 2*12.8*20.5 cos(29.3°) = 126.428
c = 11.24
Then let's use the law of sines:
a/c = sin (γ)/sin (α); b/c = sin (β)/sin (α);
Thus
γ = arcsin(a/c * sin (α)) = 33.8°

β = arcsin(b/c * sin (α)) = 63.2°

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