Question

Solve each triangle.

Short answer

The solution is$C=50°,a\approx 11.8,c\approx 9.2$.

Step-by-step solution

Step 1. Given information 

Step 2. Calculation 

We know,

$A+B+C=180°$

$100°+30°+C=180°$

$C=50°$

Now use Law of Sines -

role="math" localid="1646917225746" $\frac{\sin A}{a}=\frac{\sin B}{b}$ and role="math" localid="1646917236084" $\frac{\sin B}{b}=\frac{\sin C}{c}$

$\frac{\sin 100°}{a}=\frac{\sin 30°}{6}$ $\frac{\sin 30°}{6}=\frac{\sin 50°}{c}$

$\frac{6\sin 100°}{\sin 30°}=a$ $c=\frac{6\sin 50°}{\sin 30°}$

$11.8\approx a$ $c\approx 9.2$