A person climbs a hill in a straight path from point ‘O’ on the ground in the direction of north-east and reaches a point ‘A’ after travelling a distance of 5 km. Then, from the point ‘A’ he moves to point ‘B’ in the direction of north-west. Let the distance AB be 12 km. Now, how far is the person away from the starting point ‘O’?
Answer & explanation
Answer: (b) 13 km
North-east and north-west are at right angles, so the path turns through 90° at A. OB is the hypotenuse of a right triangle with arms 5 km and 12 km: √(5² + 12²) = 13 km.
- North-east and north-west are perpendicular, so angle OAB = 90°.
- OA = 5 km and AB = 12 km are the arms of the right angle.
- OB = √(5² + 12²) = √169 = 13 km.
Remember · Directions 90° apart (NE and NW, N and E) form a right angle — use Pythagoras; 5-12-13 is a triple worth knowing.
Question and answer: UPSC's official GS Paper II (2016, Series A) — paper ↗ · answer key ↗. Explanation: Minimalist IAS, checked 30 Sept 2026 (how we verify). ·