cos x = 0.08696

We need to use the cosine inverse to find the angle...

acos(.08696) = 85.011257976987°......Note that the cosine is positive in the 4th quadrant as well, so the angle might also be 360° - 85.011257976987° = 274.988742023013° 

Do an inverse cosine function.

cos x = 0.08696 goes to (acos(0.08696))= x

Plug (acos(0.08696))^-1 into a calculator

$$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{0.086\: \!96}}\right)} = {\mathtt{85.011\: \!257\: \!976\: \!987^{\circ}}}$$

x = 85.011 deg.