Question

What is the value of Sin 60° ?
A) √3/2
B) √3
C) 1√3
D)1/√2​

Answer 1

Step-by-step explanation:

(A) option is the correct answer....

Answer 2

Answer:

A

Step-by-step explanation:

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√ .)