how do you find the opposite side of a right triangle in trig?

Answer 1

That depends on what you do know:

If you know the hypotenuse, h, and the adjacent side x, then the opposite side y = √(h²-x²).

If you know the angle, θ, and the hypotenuse, then y = h sin(θ).

If you know the other angle, β, then y = h cos(β)

If you are given the tan(θ) and the adjacent side, x, then y = x tan(θ).