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Solution,
Given,
The ship B always remains to the north of A. This means that ship B always remains vertically upward of ship A. This is possible only when both ships cover an equal horizontal distance in time t.
So, the condition suggests that the horizontal velocity of ship B must be equal to the horizontal velocity of ship A.
The horizontal velocity of ship B = $V_B\cos \left(\theta \right)$
The horizontal velocity of ship A = $V_A$
Thus,
$\frac{V_A}{V_B}=\frac{V_B\cos \left(\theta \right)}{V_B}=\cos \left(\theta \right)$
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