Which bond angle ($\mathrm{\theta }$ ) would result in the maximum dipole moment for the triatomic molecule ${\mathrm{XY}}_2$ ?

The dipole moment of two dipole inclined at an angle $\mathrm{\theta }$ is given by the equation

$\mathrm{\mu }=\sqrt{{\mathrm{X}}^2+{\mathrm{Y}}^2+2\mathrm{XYcos\theta }} \mathrm{the} \mathrm{value} of \cos {90}^{\circ }=0\mathrm{.}$

Since the angle increases from 90-180, the value of $\mathrm{cos\theta }$ becomes more and more -ve and hence resultant decreases, thus dipole moment is maximum when $\mathrm{\theta }=90°$.