what angle has a sin of .866025403784
That is what inverse sin or arcsin is for
$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.866\: \!025\: \!403\: \!784}}\right)} = {\mathtt{59.999\: \!999\: \!999\: \!95^{\circ}}}$$
