Answer
$\Delta t = \frac{D~sin~\theta}{v}$
Work Step by Step
We can find an expression for $d$:
$\frac{d}{D} = sin~\theta$
$d = D~sin~\theta$
We can find the time it takes for the sound to travel a distance $d$:
$t = \frac{d}{v}$
$t = \frac{D~sin~\theta}{v}$
Therefore, $\Delta t = \frac{D~sin~\theta}{v}$
