To find angle A of thiagle whote sides a=9,b=4 and angle \(\displaystyle{B}={23}^{{\circ}}\)

We trigonometric identify

\(\displaystyle{\frac{{{\sin{{B}}}}}{{{b}}}}={\frac{{{\sin{{A}}}}}{{{q}}}}\Rightarrow{\frac{{{\sin{{23}}}}}{{{4}}}}={\frac{{{\sin{{A}}}}}{{{9}}}}\)

\(\displaystyle\Rightarrow{A}={61.54}°\)

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

\(\displaystyle{C}={180}-{61}-{54}-{23}\)

\(\displaystyle{C}={95.46}\)

Mow to determine side C

\(\displaystyle{\frac{{{\sin{{C}}}}}{{{c}}}}{\frac{{{\sin{{B}}}}}{{{b}}}}\)

\(\displaystyle{C}={\frac{{{\sin{{C}}}}}{{{\sin{{B}}}}}}{x}{b}\)

\(\displaystyle{C}={\frac{{{\sin{{95.46}}}}}{{{\sin{{23}}}}}}{x}{4}\)

\(\displaystyle{C}={\frac{{{3.98}}}{{{\sin{{23}}}}}}\)

\(\displaystyle{C}={10.19}\)