Himani goes 14 m towards West, then she turns right and walks 10 m, again she turn right and walks 6 m. Then finally she turns left and walks 5 m. How far and in which direction is she now from her starting point?17 m, North-West11 m, South-East17 m, North-East11 m, South-West

Himani starts by going 14 m West. Then she turns right, which would be North if we consider the standard directions, and walks 10 m. Then she turns right again, which would now be East, and walks 6 m. Finally, she turns left, which would be North, and walks 5 m.

To find out how far she is from her starting point, we need to consider her displacement in the North-South direction and the East-West direction separately.

In the East-West direction, she initially goes 14 m West, then 6 m East. So, her total displacement in the East-West direction is 14 - 6 = 8 m West.

In the North-South direction, she goes 10 m North, then 5 m North again. So, her total displacement in the North-South direction is 10 + 5 = 15 m North.

Now, we can use the Pythagorean theorem to find out how far she is from her starting point. The distance is sqrt((East-West displacement)^2 + (North-South displacement)^2) = sqrt((8 m)^2 + (15 m)^2) = sqrt(64 m^2 + 225 m^2) = sqrt(289 m^2) = 17 m.

To find out the direction, we can use the arctan function. The angle is arctan((North-South displacement) / (East-West displacement)) = arctan(15 m / 8 m) = 61.93 degrees. This angle is measured from the West, going counter-clockwise, because the East-West displacement is towards the West and the North-South displacement is towards the North. So, the direction is North-West.

So, Himani is 17 m away from her starting point in the North-West direction.