Here, two projectiles are projected at angles 42$$^\circ$$ and 48$$^\circ$$ with same initial velocity.

As we know the expression of range of projectile,

Range $$ = {{{u^2}\sin 2\theta } \over g}$$

AT $$\theta$$₁ = 42$$^\circ$$,

Range, $${R_1} = {{{u^2}\sin 2(42)^\circ } \over g} = {{0.99{u^2}} \over g}$$

At $$\theta$$₂ = 48$$^\circ$$

Range, $${R_2} = {{{u^2}\sin 2(48)^\circ } \over g} = {{0.99{u^2}} \over g}$$

The range of the projectile is same for the two projectiles.

Therefore, R₁ = R₂

Now, as we know the expression of height of the projectile,

$${H_{\max }} = {{{u^2}\sin \theta } \over {2g}}$$

At 42$$^\circ$$, $${H_{\max }} = {H_1} = {{{u^2}\sin 42^\circ } \over {2g}} = {{0.669{u^2}} \over {2g}}$$

At 48$$^\circ$$, $${H_{\max }} = {H_2} = {{{u^2}\sin 48^\circ } \over {2g}} = {{0.743{u^2}} \over {2g}}$$

Higher the value of $$\theta$$ higher the value of maximum height. Therefore, H₁ < H₂.