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 ?
An angle less than 45° North of East
According to the given information the figure is shown below,
On analyzing the above figure we get the woman travelled 12 km Northward and 6 km Southward, so she travelled 6 Km northward and she also travelled 8 Km eastward. So the direction from start point to endpoint is Northeast and angle is less than 45º as she travels more distance towards east than resultant North.
Hence, she is at a n angle less than 45° North of the East.
Key Points
- Here, we follow the theorem of the right-angled triangle where the angles other than the right angle varies with the opposite side. If the opposite side is greater than the other, then the angle opposite to the greater side is more than 45º or vice versa.
Important Questions from Direction and Distance Turns
After leaving school, Hemant and Anurag walk towards the north for 1 km to reach a bus stop. From the bus stop, Hemant turns left and walks for 500 m. Then he turns towards his left and walks for 2 km to reach his home. From the bus stop, Anurag turns right and walks for 250 m. Then he turns right and walks for 1 km to reach his home. In which direction is Anurag's home from Hemant's home?
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
Two friends Xand Ystart running and they run together for 50 m in the same direction and reach a point. Xturns right and runs 60 m, while Yturns left and runs 40 m. Then Xturns left and runs 50 m and stops, while Yturns right and runs 50 m and then stops. How far are the two friends from each other now?
Ashish cycles 11 km south, then turns west and cycles 8 km, then turns north and cycles 6 km, then turns east and cycles 2 km, then turns to his left and cycles 5 km. Where is he now with reference to his starting position?
Shekhar starts walking south from his school and then took one right turn, one left turn and one right turn to reach his shop. In which direction is Shekhar with respect to his school?
