Are you allowed to use a calculator? If so, there's a sin-1 function. You'd just sin-1(.85) and get your result. Make sure you're in degrees mode on the calculator.
If you're not supposed to use a calculator, I'm sorry, I don't know.
I missed some school due to the flu, so I missed the concept completely.
My question:
In the equation sinΘ=0.85 (In degrees, 0≤Θ≤360), how do I solve for theta?
From a calculator, $\displaystyle \Theta = 58.2^0$ (correct to 1 decimal place). From symmetry of the unit circle another solution is $\displaystyle \Theta = 180^0 - 58.2^0 = ....$