A boy cycles 10km south east and then 8 km West . How far is he from his initial position ?

Dear student,
From the figure given, ∆AOB is a right angled triangle with angle AOB=90°. So, by Pythagoras theorem, 
OA​​​​​2​​​​=OB​​2​ + AB​2 
=> OB=√(OA​​​​​2 - AB​​​​​2 )
=> OB=√(100-64) [since OA=10km and AB=8km]
=> OB=√36=6
So, he is 6km far from his initial position.

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