Question

How do you prove `sin (pi/3)`?

Answer 1

Use an equilateral triangle and the Pythagorean Theorem

Explanation:

I have assumed that the question was meant to be
`color(white)("XXX")`Prove that `sin(pi/3)= sqrt(3)/2`

An equilateral triangle has three sides of equal length and three equal angles.
(Since the angles are equal and since the interior angles of a triangle must add up to `pi` each interior angle must be `pi/3`).
If we assign a length of 2 units to each side of an equilateral triangle,
we can develop the ratio for `sin(pi/3)` as indicated below