How does this? sin

Draw a right angled triangles with angles 20 and 70 degrees.  

Convince yourself that sin70 = cos 20

Now 

$$\\sin^2 20 + sin^2 70 \\\\ =sin^2 20 + cos^2 20 \\\\ =1\\\\\\ remember\; the\; identity\\\\ \boxed{sin^2 \theta + cos^2 \theta=1}$$

$${\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{20}}^\circ\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}\left({\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}^{\,{\mathtt{2}}}\right) = {\mathtt{1}}$$

$${\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{20}}^\circ\right)}}^{\,{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{sin}}{\left({\mathtt{70}}^\circ\right)}}^{\,{\mathtt{2}}} = {\mathtt{1.000\: \!000\: \!000\: \!000\: \!398\: \!8}}$$