Question

How can you prove that sin60 degrees is root of 3 divided by 2?

Answer 1

Hello Friends,

How Sin 60 is equal to √3/2?

Construct an equilateral triangle ABC, and find the midpoint of BC, calling it D. Since triangle ABC is equilateral, all of its angles are 60∘, and line AD bisects angle A into two 30∘ angles. Hence triangle ABD is a right-angled triangle, with angle 60∘ at B. Since AB=BC and BC=2BD, we have AB=2BD. Now

AB2=AD2+BD2

(2BD)2=AD2+BD2

4BD2=AD2+BD2

3BD2=AD2

AD=(3–√)BD.

So sin60∘=ADAB=(3√)BD2BD=3√2.

(We can also show by this argument that cos60∘=12, tan60∘=3–√, sin30∘=12, cos30∘=3√2 and tan30∘=13√.)

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