Two projectiles A and B are launched with an angle of projection of...

The horizontal range of a projectile is given by $R = \dfrac{u^2 \sin(2\theta)}{g}$.

For projectile $A$, \theta_A = 15^{}^{{}^{\circ}}, so R_A = \dfrac{u_A^2 \sin(30^{}^{{}^{\circ}})}{g} = \dfrac{u_A^2}{2g}.

For projectile $B$, \theta_B = 45^{}^{{}^{\circ}}, so R_B = \dfrac{u_B^2 \sin(90^{}^{{}^{\circ}})}{g} = \dfrac{u_B^2}{g}.

Since the initial velocities $u_A$ and $u_B$ are not provided in the question, the ranges cannot be compared.

Therefore, the information is insufficient to determine the relation between $R_A$ and $R_B$.