Two projectiles are fired from the ground with the same initial...

The maximum height of a projectile is given by $H = \dfrac{u^2 \sin^2\theta}{2g}$.

For the first projectile fired at an angle $\theta$:
$H_1 = \dfrac{u^2 \sin^2\theta}{2g}$

For the second projectile fired at an angle $(90^\circ - \theta)$:
$H_2 = \dfrac{u^2 \sin^2(90^\circ - \theta)}{2g} = \dfrac{u^2 \cos^2\theta}{2g}$

The sum of their maximum heights is:
$H_1 + H_2 = \dfrac{u^2 \sin^2\theta}{2g} + \dfrac{u^2 \cos^2\theta}{2g}$

$H_1 + H_2 = \dfrac{u^2}{2g} (\sin^2\theta + \cos^2\theta)$

Using the trigonometric identity $\sin^2\theta + \cos^2\theta = 1$, we get:
$H_1 + H_2 = \dfrac{u^2}{2g}$

Answer: $\dfrac{u^2}{2g}$