You need to know some basic physics, namely the kinematic equations. The only force is gravity, acting downwards (negative y direction), producing an acceleration g=9.8 m/s^2. Thus the position as a function of time, using our start as the origin, is given by , , where and are the x and y components of the launch velocity, respectively.

y(t)=0 when the projectile hits the ground, so solve that for t (there is a t=0 solution, which is because the projectile is launched from the ground; you want the nonzero solution). Plug this into x(t) to get the range as a function of , , and g. and can in turn be expressed in terms of the launch velocity and launch angle. You thus have an equation relating the unknown to the known range, launch angle, and acceleration of gravity.

--Kevin C.