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CBSE - Mathematics - Triangles

Triangles

NCERT Exercise Exercise 6.5

 An aeroplane leaves an airport and flies due north at a speed of 1,000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1,200 km per hour. How far apart will be the two planes after  hours?

Speed of first aeroplane = 1000 km/hr

Distance covered by first aeroplane due north in  hours (OA) = 100 × 3/2 km = 1500 km

Speed of second aeroplane = 1200 km/hr

Distance covered by second aeroplane due west in hours (OB) = 1200 × 3/2 km = 1800 km

In right angle ΔAOB, we have

AB2 = AO2 + OB2

⇒ AB2 = (1500)2 + (1800)2

⇒ AB = √2250000 + 3240000

            = √5490000

⇒ AB = 300√61 km

Hence, the distance between two aeroplanes will be 300√61 km.

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