Question

how can the value of tan30 be found?

Answer 1

ou need to know first of all that tanx=sinx/cosx

You will also need to know that:
sin0=0
sin30=1/2
sin45=sqrt[2]/2
sin60=sqrt[3]/2
sin 90 =1

and
cos0=1
cos30=sqrt[3]/2
cos 45=sqrt[2]/2
cos60=1/2
cos90=0

so you can recognize that 1/sqrt[3] corresponds to tan30, since tan30=sin30/cos30
=1/2/sqrt[3]/2 = 1/sqrt[3]