90. Are the conditions of the problem really incomplete? Someone, not paying close attention to the previous problem, recounted it to Dr. Sharadek and asked how to determine the course based on the conditions of the problem. Unfortunately, he forgot which of the ships had the greater speed and which had the lesser, but he remembered that the ratio of speeds $k$ was known and less than 1. However, he did not know whether $k$ represented the ratio of the signaling ship's speed to the observed ship's speed or vice versa. To his great surprise, the master immediately determined the course based on the incomplete data! How did Dr. Sharadek manage to do this?
90. If $k$ has the same value as in the previous problem, then the course of the signaling ship is determined by the angle $\alpha$ (Fig. 164) as follows:

$$
\sin \alpha=k=\frac{v_{1}}{v_{2}}
$$

Fig. 164.

If, on the contrary, $k$ denotes the ratio of the speed of the detected ship to the speed of the signaling ship, then when the course is again determined by the equation $\sin \alpha=k$, the ships will meet at point $O_{2}$ (Fig. 164), because

$$
\frac{P_{1} O_{2}}{v_{1}}=\frac{P_{2} O_{2}}{v_{2}}
$$

or

$$
\begin{aligned}
\frac{1}{v_{1} \cos \alpha} & =\frac{\operatorname{tg} \alpha}{v_{2}} \\
\sin \alpha & =\frac{v_{2}}{v_{1}}=k
\end{aligned}
$$

Therefore, in the second case, the course is determined in the same way as in the first.