Algebra 2, please help

Question

If cos squared a = 3/8 what’s an expression for sin a?

Answer 1

cos² a + sin² a = 1

3 / 8 + sin² a = 1

sin² a = 5 / 8

sin a = √5 / √8

You can simplify the radical.

Answer 2

If you know that cos² a =3/8, then if you take the square root of both sides, you have cos a = √(3/8). This tells you that the adjacent leg the triangle has a length of √3 and the hypotenuse is √8. According to the pythagorean theorem, the remaining leg of the triangle (opposite to the angle), must be √5. Since sin a = opp/hyp, then sin a = √(5/8).