Question

find the length of side c.
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{c}{\sin C}$.

Step2: Substitute the known values

We know that $a = 10.8$, $A=120^{\circ}$, and $C = 20^{\circ}$. Substituting into the formula gives $\frac{10.8}{\sin 120^{\circ}}=\frac{c}{\sin 20^{\circ}}$.

Step3: Solve for $c$

First, calculate $\sin 120^{\circ}=\frac{\sqrt{3}}{2}\approx0.866$ and $\sin 20^{\circ}\approx0.342$. Then, from $\frac{10.8}{0.866}=\frac{c}{0.342}$, we can cross - multiply: $c=\frac{10.8\times0.342}{0.866}$.
Calculate $10.8\times0.342 = 3.6936$. Then $c=\frac{3.6936}{0.866}\approx4.3$.

Answer:

$4.3$