should be possible, let me try to solve it right here...
assuming you start at x=0, and land at x=r, given cc angle a, you have:
vy/vx = tan a,
y = vy * t - g * t * t,
x = vx * t.
put 3rd into 2nd:
y = x tan a - x^2 * (g / vx^2)
the height would be y when x=r/2:
h = (r/2) tan a - (r/2)^2 * (g / vx^2)
now to find (g / vx^2) remember that y(x=r)=0:
0 = r tan a - r^2 * (g / vx^2)
or
(g / vx^2) = (r tan a) / (r^2) = (tan a) / r
so, finally,
h = (r/2) tan a - (r/2)^2 * (tan a) / r = (r/2 - r/4) tan a = (r/4) * tan a