A man walked 3km towards North, turned
West and walked 2km, then turned North
again and walked 1km and then turned East
and walked 5km. How far is he from his
starting point--
Answers
Starting point P.
1st travelling towards North
from point P to A=S1= 3 km
2nd travelling towards West
from A to B = S2= 2 km
3rd travelling towards North
from B to C = S3= 1 km
4th travelling towards East
from C to E1 =S4= 5 km
Joining all these points, finally we get a triangle from starting point P to the final destination E1 after covering a distance of 5 km to the East. The position of the traveller is now point E1, North-East (NE) position which is a diagonal measurement of the trianglar path from starting point P to E1.
Starting point P to North-East position E1:
Distance covered =d2= S1 + S3
d2 = 3 km + 1 km = 4 km
Length of triangluar side from West to East DE1:
d1 = DE1= S4 - S2 = 5 - 2 = 3 km
Using Pythagorean’s theorem:
d1^2 + d2^2 = PE1^2
4^2 + 3^2 = PE1^2
PE1^2 = 16 + 9 = 25
PE1 = 5 km
Answer:
The traveller is at a distance PE1 = 5 km from starting point to the end point E1 in the North-East direction.
