Solution :
The value of sin 30 degrees is 12.
Proof :
Consider an equilateral triangle ABC with each side of length of 2a. Each angle of Δ ABC is of 60 degrees. Let AD be the perpendicular from A on BC.
∴ AD is the bisector of ∠ A and D is the mid-point of BC.
∴ BD = DC = a and ∠ BAD = 30 degrees.
In Δ ADB, ∠ D is a right angle, AB = 2a and BD = a
By Pythagoras theorem,
AB2 = AD2 + BD2 ⟹ 2a2 = AD2 + a2
⟹ AD2 = 4a2 – a2 = 3a2 ⟹ AD = √3a
Now, In triangle ADB, ∠ BAD = 30 degrees
By using trigonometric formulas,
sin30∘ = perpendicularhypotenuse = ph
sin30∘ = side opposite to 30 degrees/hypotenuse = BDAB = a2a = 12
Hence, the value of sin30∘ = 12