Ragini facing East walks 10 meter, then she turns to her left and walks 12 meter. Then she turns to her right in $45^o$ and walks 15 meter. Then, how much distance she has walked from the starting point and which direction is she facing now ?
37 meter, North-East
The question has two parts, and each is settled separately.
Distance walked. The stem asks how much distance she has walked, so add the three legs of her journey: \(10 + 12 + 15 = 37\) metres. This is the total path length she covers on foot, not the straight-line gap between her start and finish.
Direction faced. Track the turns one at a time. She begins facing East. Turning to her left from East swings her a quarter turn anticlockwise, so she now faces North, and she covers 12 metres in that direction.
She then turns to her right through 45°, which is half a quarter turn clockwise from North. Half-way between North and East is North-East, and she walks the final 15 metres facing that way.
Hence she has walked 37 metres and is now facing North-East.
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