## Trigonometry (11th Edition) Clone

$A = 49^{\circ}30'$
We can use the law of sines to find angle $A$: $\frac{a}{sin~A} = \frac{c}{sin~C}$ $sin~A = \frac{a~sin~C}{c}$ $A = arcsin(\frac{a~sin~C}{c})$ $A = arcsin(\frac{(75.3~mm)~sin~79^{\circ}20'}{97.4~mm})$ $A = arcsin(0.7597)$ $A = 49.44^{\circ} = 49^{\circ}30'$ Note that another possible value for angle $A$ could be $180^{\circ}- 49^{\circ}30'$ which is $130^{\circ}30'$ However, then angle A and angle C sum to more than $180^{\circ}$ so this is not an acceptable value for angle A.