Two ships leave a port at the same time. One goes 24 $k m / h r$ in the direction N $38^{\circ}$ E and other travels 32 $k m / h r$ in the direction S $52^{\circ}$ E. Find the distance between the ships at fine end of 3 hrs.

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Solution

$Let P and Q be the position of two ships at the end of 3 hours. T h e n, O P = 3 \times 24 = 72 k m a n d O Q = 3 \times 32 = 96 k m Using cosine formulat in Δ O P Q, we get P Q^{2} = O P^{2} + O Q^{2} - 2 O P \times O Q c o s 90^{\circ} P Q^{2} = 72^{2} + 96^{2} - 2 \times 72 \times 96 c o s 90^{\circ} P Q^{2} = 14400 P Q = 120 k m$

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