How do you solve the equation

5√3 secθ = 10 in degree measure?

please explain.

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°