# Application of pythagoras theorem on the following scenario

Sam goes $\sqrt{12.5}$ km towards west from a certain point. Then after turning to his right he again goes same distance. In the end he goes 25 km towards south-east. How far is he from the starting point.

Isn't he at the origin point (i.e. from where he started) or am I mistaken?

-
Doesn't this depend on knowing which way he was facing to start with (i.e., what is the relationship between the directions "west" and "to his right")? – Zev Chonoles Jul 1 '12 at 14:34
does it matter which side he was facing initially.I am assuming he started towards the west (typical compass style) and then moved to his right from there. – Joe Jul 1 '12 at 14:50
He could have been going west while facing in any direction (though perhaps one is supposed to assume he was facing west). – Zev Chonoles Jul 1 '12 at 14:57
@Joe: Maybe the typo was not in the answer but in the question. If goes $5$ km SE, then distance is indeed $20$. – André Nicolas Jul 1 '12 at 14:59
The question didn't contain the direction he was facing, but wouldn't the answer be the same irrespective of the direction he was facing. Kindly clarify? – Joe Jul 1 '12 at 15:01

The way the question is currently stated, Sam winds up 20km from the starting point.

Call the starting point $A$.

Sam goes $\sqrt{12.5}$km west and gets to a point we'll call $B$.

Sam goes $\sqrt{12.5}$km north and gets to a point we'll call $C$.

Now $ABC$ is an isosceles right triangle with right angle at $B$ (we are ignoring curvature of the Earth here, and treating it as a plane. If Sam started $\sqrt{12.5}$km south of the North Pole, all bets are off). By Pythagoras, $A$ is 5km southeast of $C$. So if Sam now goes 25km to the southeast, he goes 20km past $A$, winding up 20km from the starting point.

-
So the originally stated answer of 20 km is correct. – Joe Jul 2 '12 at 7:16
Looks that way to me. – Gerry Myerson Jul 2 '12 at 9:18

Correct. He traverses the edges of a 45-45-90 triangle. Your answer is right.

-
The answer was mistakenly provided as 20 km(s) for the above question. Guess it was incorrect. – Joe Jul 1 '12 at 14:49