Posted by John on Thursday, October 4, 2012 at 11:08am.
secØ = 10/5√3 = 2/√3
then
cosØ = √3/2
You should be familiar with the 1 : √3 : 2 right-angled triangle which has angles of 30:60:90
thus Ø = 30°
but the cosine is also positive in the fourth quadrant
so Ø could be 330°
Ø = 30° or Ø = 330°