Question

explain and show the trigonometric ratios of triangle 45°and30° ..with pythagoras theorem

Answer 1

hope it will help you out

Answer 2

If remember that
sin =opposite/hypotenuse
cos =adjacent/hypotenuse
tan =opposite/adjacent
and their reciprocals.

Then, for example:
sin(60o)=√3/2
sin(30o)=1/2
sin(45o)=1/√2
cos(60o)=1/2etc.