Step-by-step explanation:
Take an equilateral triangle of side.
Bisec it through a vertex and the midpoint of the opposite side.
You now have two right-angled triangles with angels 30° , 60°, 90° with the edge opposite the 30° of length 1/2 and hypotenuse 1. So
sin (30°) = 1/2/1= 1/2.
Answer: The right angled triangle you describe has angels of 45 degrees, not 30 degrees.
What you proved is sin 45 = 1\2 , which is correct.
