Answer to Question #1203 in Trigonometry for Ali

Question

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.

Answer 1

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°