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It is down to trigonometry. You have two parts of a triangle, so you are looking for the length of the last line. As the man turned right, there will be a right angle in the triangle. As we have two sides, the 12m and 5m, using Pythagoras theorem we can work out the length of the last side. The square of the hypotenuse is equal to the square of the other two sides. 12 x 12 = 144. 5 x 5 = 25. 144 + 25 = 169. 13 x 13 = 169. So the length of the other side is 13.

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Q: When a man walks 5m towards east and turns right and moves 12m the magnitude of his displacement is 13m how?
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