How to find an angle if its sine is 2√6 / 3.

Let’s write this angle:

sin x = (2√6) / 3.

Let’s try to simplify the number (2√6) / 3:

sin x = (2√6) / 3,

sin x = (2√ (3 * 2)) / (√3 * √3),

sin x = (2 √2) / √3, √2 ≈ 1.41, √3 ≈ 1.73, substitute:

sin x = (2 * 1.41) / 1.73,

sin x = (2, 82) / 1, 73,

sin x = 1, 63 – there is no solution, since the sine cannot be greater than zero.

Answer: the sine of any angle cannot be greater than 1.