Verified answer

The double-angle formula says that sin (2x) = 2 * sin(x) * cos(x).

If we take x to be 60, then the double-angle formula gives:

sin (120) = 2 * sin(60) * cos(60).

Sin(60) = sqrt(3) / 2, and cos(60) = 1/2, so this means

sin(120) = 2 * (sqrt(3) / 2) * (1/2) = (sqrt(3)/2).

sin 120 = sin(2*60) = 2*sin 60*cos 60 = 2 * sqrt(3)/2 * 0.5 = sqrt(3)/2.

(Of course, its a bit of a silly question, since if you know that sin 60 is sqrt(3)/2, you'd know straight away that sin 120 = sqrt(3)/2 as well, because sin x = sin(180-x).)

treat 120 degrees as 2x then x would be 60 degrees

sin (2x) = 2sin(x)cos(x)

sin 120 = 2sin(60degrees)cos(60degrees)

sin 120 = 2 ((square root of 3)/2)(1/2)

sin 120 = (square root of 3)/2

which is approximately 1.732 / 2 = 0.866

sin(120) = sin(2(60)) = 2sin(60)cos(60) = 2(sqrt(3)/2)(1/2) = (sqrt(3))/2

sin(120) = (sqrt(3))/2

that is an obtuse angle