Two projectiles are fired at different angles with the same magnitude of velocity, such that they have the same range. At what angles they might have been projected ?

We know that,  $\mathrm{R}=\frac{{\mathrm{u}}^2\sin 2\mathrm{\theta }}{\mathrm{g}}$

Given that, ${\mathrm{R}}_1={\mathrm{R}}_2\text{ and }{\mathrm{u}}_1={\mathrm{u}}_2$

$\begin{array}{l}\therefore {\mathrm{R}}_1=\frac{{{\mathrm{u}}_1}^4\sin 2\mathrm{\theta }}{\mathrm{g}}\\ \text{ and }{\mathrm{R}}_2=\frac{{{\mathrm{u}}_2}^2\sin 2\left({90}^{\circ }-\mathrm{\theta }\right)}{\mathrm{g}}\\ \therefore \sin 2\mathrm{\theta }=\sin 2\left({90}^{\circ }-\mathrm{\theta }\right)=\cos 2\mathrm{\theta }\end{array}$

Solving we get, $\theta ={25}^{\circ }.$ The other angle is ${90}^{\circ }-{25}^{\circ }={65}^{\circ }$