find the length of side c.\nround to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. Here, we know side $a = 10$ (opposite angle $A = 73.2^{\circ}$), angle $C=56.8^{\circ}$, and we want to find side $c$ (opposite angle $C$). So, $\frac{c}{\sin C}=\frac{a}{\sin A}$.

Step2: Substitute the values

Substitute $a = 10$, $A = 73.2^{\circ}$, and $C = 56.8^{\circ}$ into the formula: $c=\frac{10\times\sin(56.8^{\circ})}{\sin(73.2^{\circ})}$.

Step3: Calculate the sines

We know that $\sin(56.8^{\circ})\approx0.837$ and $\sin(73.2^{\circ})\approx0.958$. Then $c=\frac{10\times0.837}{0.958}$.

Step4: Compute the value of (c)

$c=\frac{8.37}{0.958}\approx8.7$.

Answer:

$8.7$