# Solve each of the following triangles. If there are two

Solve each of the following triangles. If there are two triangles, solve both. Round angle measurements to one decimal place and side lengths to two decimal places. $$\displaystyle{a}={9},{b}={4},{B}={23}^{{\circ}}$$
a=
y=
c=

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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
$$\displaystyle{\frac{{{\sin{{C}}}}}{{{c}}}}{\frac{{{\sin{{B}}}}}{{{b}}}}$$
$$\displaystyle{C}={\frac{{{\sin{{C}}}}}{{{\sin{{B}}}}}}{x}{b}$$
$$\displaystyle{C}={\frac{{{\sin{{95.46}}}}}{{{\sin{{23}}}}}}{x}{4}$$
$$\displaystyle{C}={\frac{{{3.98}}}{{{\sin{{23}}}}}}$$
$$\displaystyle{C}={10.19}$$