The length of the side x is 63.652.
Given:
Angle C = 97 degree.
Angle A = 47 degree.
The length of the side y is, 51.2 cm.
The objective is to find the length of the side x.
Consider the third side of the triangle as z.
By law of sines,
[tex]\frac{x}{\sin A}=\frac{y}{\sin B}=\frac{z}{\sin C}[/tex]
The measure of angle B can be calculated by angle sum property of triangle.
[tex]\begin{gathered} \angle A+\angle B+\angle C=180^0 \\ 47^0+\angle B+97^0=180^0 \\ \angle B=180^0-47^0-97^0 \\ \angle B=36^0 \end{gathered}[/tex]
Now the value of x can be calculated by substituting the obtained values in the first two ratios of law of sines.
[tex]\begin{gathered} \frac{x}{\sin47^0}=\frac{51.2}{\sin36^0} \\ \frac{x}{0.731}=\frac{51.2}{0.588} \\ x=\frac{51.2}{0.588}\cdot0.731 \\ x=63.652 \end{gathered}[/tex]
Hence, the length of the side x is 63.652.
