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What is the Value of Sin 30 Degrees ?

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.equilateral triangle

   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 = 4a2a2 = 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

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