Question

Solve each triangle.

Short answer

The solution is$A=40°,a\approx 2,c\approx 3.1$.

Step-by-step solution

Step 1. Given information 

Step 2. Calculation 

We know,

$A+B+C=180°$

$A+40°+100°=180°$

$A=40°$

Now use Law of Sines -

role="math" localid="1646916753582" $\frac{\sin A}{a}=\frac{\sin B}{b}$ and role="math" localid="1646916765657" $\frac{\sin B}{b}=\frac{\sin C}{c}$

$\frac{\sin 40°}{a}=\frac{\sin 40°}{2}$ role="math" localid="1646916964723" $\frac{\sin 40°}{2}=\frac{\sin 100°}{c}$

$\frac{2\sin 40°}{\sin 40°}=a$ $c=\frac{2\sin 100°}{\sin 40°}$

$2=a$ $c\approx 3.1$