A Woman at a Point $A$ On the Shore of a Circular Lake with Radius

Essay

A woman at a point $A$ on the shore of a circular lake with radius $4 \mathrm { mi }$ wants to arrive at the point $C$ diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of $6 \mathrm { mi } / \mathrm { h }$ and row a boat at $2 \mathrm { mi } / \mathrm { h }$ . How should she proceed? (Find $\theta$ ). Round the result, if necessary, to the nearest hundredth.