Two ships leave a port at the same time. One goes 24 km/hr in the direction N 38° E and other travels 32 km/hr in the direction S 52° E. Find the distance between the ships at the end of 3 hrs.

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Solution

$After three hours, let the ships be at P and Q respectively . Then, O P = 24 \times 3 = 72 km and O Q = 32 \times 3 = 96 km From figure, we have ∠ P O Q = 180 ° - ∠ N O P - ∠ S O Q = 180 ° - 38 ° - 52 ° = 90 ° Now, Since O P Q is a right angled triangle ∴ P Q^{2} = O P^{2} + O Q^{2} \Rightarrow P Q^{2} = 72^{2} + 96^{2} \Rightarrow P Q^{2} = 5184 + 9216 \Rightarrow P Q^{2} = 14400 \Rightarrow P Q = \sqrt{14400} = 120 km Hence, the distance between the ships after 3 hours is 120 km .$

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