Research ratios

The equalateral triangle above has sides each 2 units long and all angles at 60o. It has been halved into 2 right - angled triangles of base 1 unit long. Using Pythagorus:
(ab)2 = (ac)2 + (bc)2
=> (2)2 = (ac)2 + (1)2
=> (ac)2 = 4 - 1 = 3
and (ac) = root 3.
Using the definitions of trigonometrical ratios, summarised in SOHCAHTOA:
sin 30o = bc / ab = 1 / 2
sin 60o = ac / ab = root 3 / 2
cos 30o = ac / ab = root 3 / 2
cos 60o = bc / ab = 1 /2
tan 30o = bc / ac = 1 / root 3
tan 60 = ac / bc = root 3 / 1 = root 3