Solve a/sinA=4/sqrt{3/2}

$$\frac { a } { \sin A } = \frac { 4 } { \frac { \sqrt { 3 } } { 2 } }$$

Solve for a

$$a=\frac{8\sqrt{3}\sin(A)}{3}$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }A=\pi n_{1}$$

Steps for Solving Linear Equation

The equation is in standard form.

$$\frac{1}{\sin(A)}a=\frac{8}{\sqrt{3}}$$

Divide both sides by \left(\sin(A)\right)^{-1}.

$$\frac{\frac{1}{\sin(A)}a\sin(A)}{1}=\frac{8\sqrt{3}}{3\times \frac{1}{\sin(A)}}$$

Dividing by \left(\sin(A)\right)^{-1} undoes the multiplication by \left(\sin(A)\right)^{-1}.

$$a=\frac{8\sqrt{3}}{3\times \frac{1}{\sin(A)}}$$

Divide \frac{8\sqrt{3}}{3} by \left(\sin(A)\right)^{-1}.

$$a=\frac{8\sqrt{3}\sin(A)}{3}$$

Solve for A

$$A=arcSin(\frac{1}{8}\times 3^{\frac{1}{2}}a)+2\pi n_{12}\text{, }n_{12}\in \mathrm{Z}$$

$$A=\pi +2\pi n_{21}+\left(-1\right)arcSin(\frac{1}{8}\times 3^{\frac{1}{2}}a)\text{, }n_{21}\in \mathrm{Z}$$