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 ?

Explanation:

1. Calculate Net North-South Displacement:

   • The woman runs 12 km North, then 6 km South.
   • Net North displacement = 12 km - 6 km = 6 km North.

2. Calculate Net East-West Displacement:

   • She runs 8 km East. There is no West movement.
   • Net East displacement = 8 km East.

3. Determine General Direction:

   • From her starting point, she is 8 km East and 6 km North. This places her in the North-East quadrant. Therefore, the direction will be "North of East". This eliminates options A and C.

4. Calculate the Angle:

   • Let the angle (theta) be with respect to the East direction.
   • We can use the tangent function: tan(theta) = (Opposite side) / (Adjacent side)
   • Opposite side (North displacement) = 6 km
   • Adjacent side (East displacement) = 8 km
   • tan(theta) = 6 / 8 = 3 / 4 = 0.75

5. Compare the Angle with 45 degrees:

   • We know that tan(45°) = 1.
   • Since tan(theta) = 0.75, which is less than 1, the angle theta must be less than 45°.

6. Combine Direction and Angle:

   • The direction is North of East, and the angle is less than 45°.
   • This matches option B: "An angle less than 45° North of East".

Final Check of Options: A) An angle less than 45° South of East - Incorrect, as she is North of East. B) An angle less than 45° North of East - Correct, as calculated. C) In angle more than 45° South of East - Incorrect, as she is North of East and the angle is less than 45°. D) An angle more than 45° North of East - Incorrect, as the angle is less than 45°.

The final answer is B.