Height of a balloon

ay = -9.8. Vy = -9.8 + v0*Sin0. y = -4.9*t^2 + v0*t*Sin0. By using formula of y, my solution was -4.9(10s)^2 + (10m/s)(10s)Sin0. I assumed that y was equal to 0. Since -4.9 is m/s^2 the answer would be -490m + 100m*Sin0. Therefore I assumeed Sin0 = 490/100.

Your "relevant equation" does not match your problem description.
Your equation is used for a situation where there is a horizontal component to the velocity of the object in free flight.
But the problem you stated does not presume any horizontal motion - nor would it be affected by horizontal motion.
When I solve the problem as stated by you, I do not get 485 meters, nor do I get anything similar to your calculation, nor do I use trigonometry.

.Scott said:

Your "relevant equation" does not match your problem description.

At least not without specification. To use it, you must argue theta to be 90 deg., then it is correct. But it is a good idea to understand and define each element in the equation.....which you do not do. A free body diagram might be a better start .....

I agree (with @hutchphd) . When theta is taken as 90 degrees, then "Sin0" is 1 and the calculation in the second-to-last statement (of @tremain74 ) is correct.
But what is "Therefore I assumed Sin0 = 490/100." supposed to mean? Even if you are trying to force it to the answer provided (the apparently incorrect 485m), that statement would not be true.