Step 1

We know that the sum of angles in a triangle equals \(\displaystyle{180}^{{\circ}}\) degrees. Therefore,

\(\displaystyle\angle{B}{A}{C}+\angle{C}{B}{A}+\angle{A}{C}{B}={180}^{{\circ}}\)

\(\displaystyle\angle{C}{B}{A}={180}^{{\circ}}-\angle{B}{A}{C}-\angle{A}{C}{B}\)

\(\displaystyle\angle{C}{B}{A}={180}^{{\circ}}-{44}^{{\circ}}-{103}^{{\circ}}\)

\(\displaystyle\angle{C}{B}{A}={33}^{{\circ}}\)

Step 2

By using law of sines in the given triangle,

\(\displaystyle{\frac{{{\sin{\angle}}{B}{A}{C}}}{{{x}}}}={\frac{{{\sin{\angle}}{C}{B}{A}}}{{{y}}}}\)

\(\displaystyle{\frac{{{\sin{{44}}}^{{\circ}}}}{{{x}}}}={\frac{{{\sin{{33}}}^{{\circ}}}}{{{50.5}}}}\)

\(\displaystyle{x}={\frac{{{\sin{{44}}}^{{\circ}}}}{{{\sin{{33}}}^{{\circ}}}}}\times{50.5}\)

\(\displaystyle{x}={\frac{{{0.6946}}}{{{0.5446}}}}\times{50.5}\)

\(\displaystyle{x}={64.41}\)

The value of x is therefore 64.41 cm

We know that the sum of angles in a triangle equals \(\displaystyle{180}^{{\circ}}\) degrees. Therefore,

\(\displaystyle\angle{B}{A}{C}+\angle{C}{B}{A}+\angle{A}{C}{B}={180}^{{\circ}}\)

\(\displaystyle\angle{C}{B}{A}={180}^{{\circ}}-\angle{B}{A}{C}-\angle{A}{C}{B}\)

\(\displaystyle\angle{C}{B}{A}={180}^{{\circ}}-{44}^{{\circ}}-{103}^{{\circ}}\)

\(\displaystyle\angle{C}{B}{A}={33}^{{\circ}}\)

Step 2

By using law of sines in the given triangle,

\(\displaystyle{\frac{{{\sin{\angle}}{B}{A}{C}}}{{{x}}}}={\frac{{{\sin{\angle}}{C}{B}{A}}}{{{y}}}}\)

\(\displaystyle{\frac{{{\sin{{44}}}^{{\circ}}}}{{{x}}}}={\frac{{{\sin{{33}}}^{{\circ}}}}{{{50.5}}}}\)

\(\displaystyle{x}={\frac{{{\sin{{44}}}^{{\circ}}}}{{{\sin{{33}}}^{{\circ}}}}}\times{50.5}\)

\(\displaystyle{x}={\frac{{{0.6946}}}{{{0.5446}}}}\times{50.5}\)

\(\displaystyle{x}={64.41}\)

The value of x is therefore 64.41 cm