Question

A man runs 40 m towards west, then 20 m towards south. He then runs another 40 m towards east. In
which direction is he from his starting point?​

Answer 1

Step-by-step explanation:

65 meters north west.

Step-by-step explanation:

Since, north is left to east, east is left to south, south is left to west and west is left to north,

Also, north is right to west, west is right to south, south is right to east and east is right to north,

Let O be the initial position of man,

Now, after going 40m towards north man's position is A,

Then after taking left and going 40m, his position is B,

After again going 15 m left his position is C,

Finally, his final position after going 20 m right, his position is D,

By making the diagram,

We observed,

D is north west to O.

Also, suppose L ∈ AO

Such that, AL = BC = 15 m,

⇒ LO = OA - AL = 40 - 15 = 25 m,

Also, DL = DC + CL = 20 + AB = 20 + 40 = 60 m,

By Pythagoras theorem,

OD^2 = DL^2 + OL^2 = 60^2 + 25^2 = 3600 + 625 = 4225OD

2

=DL

2

+OL

2

=60

2

+25

2

=3600+625=4225

\implies OD = 65\text{ m}⟹OD=65 m