+564 $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{60}}^\circ\right)} = {\frac{{\mathtt{x}}}{{\mathtt{12}}}}$$
$${\mathtt{12}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{60}}^\circ\right)} = {\mathtt{x}}$$
$${\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}} = {\mathtt{x}}$$
If you want to check the solution, refer back to the unit circle. $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{60}}^\circ\right)}$$ on the unit circle is $${\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}$$. When you put $${\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}$$ in place of x for the $${\frac{{\mathtt{x}}}{{\mathtt{12}}}}$$, you get $${\frac{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}\right)}{{\mathtt{12}}}}$$. Simplify that number further and you get $${\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}$$.
.+564 $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{60}}^\circ\right)} = {\frac{{\mathtt{x}}}{{\mathtt{12}}}}$$
$${\mathtt{12}}{\mathtt{\,\times\,}}\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{60}}^\circ\right)} = {\mathtt{x}}$$
$${\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}} = {\mathtt{x}}$$
If you want to check the solution, refer back to the unit circle. $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{60}}^\circ\right)}$$ on the unit circle is $${\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}$$. When you put $${\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}$$ in place of x for the $${\frac{{\mathtt{x}}}{{\mathtt{12}}}}$$, you get $${\frac{\left({\mathtt{6}}{\mathtt{\,\times\,}}{\sqrt{{\mathtt{3}}}}\right)}{{\mathtt{12}}}}$$. Simplify that number further and you get $${\frac{{\sqrt{{\mathtt{3}}}}}{{\mathtt{2}}}}$$.
