Answer
$R=310.56$ feet.
$H=77.64$ feet.
Work Step by Step
$R=\frac{v_0^2\sin{(2\theta)}}{g}=\frac{100^2\sin{(2\cdot45^\circ)}}{32.2}=\frac{10000\cdot1}{32.2}\approx310.56$ feet.
$H=\frac{v_0^2\sin^2{(\theta)}}{2g}=\frac{100^2\sin^2{(45^\circ)}}{2\cdot32.2}=\frac{10000\cdot({\frac{1}{\sqrt2})^2}}{2\cdot32.2}\approx77.64$ feet.
