information:extraction, information:classification, information:highlighting, stylistic:style_transfer
Example 1

Given: side a = 20, side c = 24, and angle γ = 40°. Angle α is desired.

Using the law of sines, we conclude that sin α 20 = sin (40 ∘) 24. {\displaystyle {\frac {\sin \alpha }{20}}={\frac {\sin(40^{\circ })}{24}}.} α = arcsin (20 sin (40 ∘) 24) ≈ 32.39 ∘. {\displaystyle \alpha =\arcsin \left({\frac {20\sin(40^{\circ })}{24}}\right)\approx 32.39^{\circ }.}

Note that the potential solution α = 147.61° is excluded because that would necessarily give α + β + γ > 180°.