Answer
6.04 m.
Work Step by Step
Use Snell’s Law to find the angle of incidence for refraction from the water into the air.
$$n_{water}sin \theta_i=n_{air}sin \theta_r$$
From the diagram given in the problem, we see that the refracted angle is $77^{\circ}$. Remember, we measure all angles off the normal to the surface.
$$1.33sin \theta_i=1.00sin77^{\circ}$$
$$ \theta_i=47.11^{\circ}$$
From the diagram given in the problem, we find the depth D of the pool.
$$tan 47.11^{\circ}=\frac{6.50m}{D}$$
$$D=6.04m$$