PHYSICS: How do you find the range, R?

Do you want the final result or complete derivation?

The result is

R = v0^2 * sin(2 theta)/g

First go to your physics book and find your equations for kinematics, as they govern projectile motion. I will be refering to these equations frequently.

Lets start with the initial velocity. We need the components of it, this is simple trig since we know the angle. Vertically we have

v0 * sin(theta)

Horizontally you should get

v0 * cos(theta)

Now lets look at motion in the vertical direction. The height of the projectile is governed by

y = y0 + v0 * sin(theta) * t + 1/2 * g * t^2

This equation should be in your book. y0 is your initial height, which is zero. When the ball lands, y is also zero. The only unknown is t. I suggest using the quadratic equation to solve for it, since you are working in variables. It will give 2 solutions, since the ball is at zero at launch and at landing.

Now that we know how long the ball is in the air (t), we can look at the horizontal direction. The equation is the same, except that there is no acceleration:

R = x0 + v0 * cos(theta) * t , where R is the range.

x0 is zero, all that is left is to plug in t from above and you've got it. This procedure works for all projectile problems, by the way.