You walk 51m to the north, then turn 60° to your right and walk another 45 how far are you from where you originally started

The resultant displacement, R = 83.19 m

Explanation:

Given,

The displacement towards the north, P = 51 m

The displacement towards the north-east 60°, Q = 45 m

The angle between two vectors, ∅ = 60°

The resultant displacement, 'R' is given by the formula of addition of vectors

                              R = √(P² + Q² + 2PQ cos∅)

Substituting the given values in the above equation

                              R = √(51² + 45² + 2x51x45 cos 60)

                                 = √(6121)

                                 = 83.19 m

Hence, the distance between the initial and final position is, R = 83.19 m

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