Q. A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point?
(a) An angle less than 45o South of East
(b) An angle less than 45o North of East
(c) An angle more than 45o South of East
(d) An angle more than 45o North of East
Correct Answer: (b) An angle less than 45o North of East
Question from UPSC Prelims 2021 CSAT Paper
Explanation :
A woman runs 12km
Initial position: (0,0)
Movements:
1. North 12 km → (0,12)
2. South 6 km → (0,6)
3. East 8 km → (8,6)
Final position: (8,6)
Direction calculation of women:
– Angle = tan⁻¹(6/8)
– Angle = tan⁻¹(0.75)
– Angle = 36.87°
Since:
– tan 45° = 1
– 6/8 = 0.75 < 1
– Therefore, angle is less than 45°
