Physics
posted by Jacqueline .
A scout troop is practicing its orientation skills with a map and compass. First they walk east for 1.2km. Next, they walk 45degrees west of north for 2.7km. In what direction must they walk to go directly back to their starting point? How far will they have to walk?

The vector to the final location from the starting point has components of 1.2  2.7 sin 45 = 0.709 km in the east direction and 2.7 sin 45 = 1.909 in the north direction. The direction they must walk back is the reverse of that vector. You can use the ratio of the two components to get the tangent of the angle.
The distance is the hypotenuse, sqrt[(0.709)^2 + (1.909)^2] = 2.04 km 
thank you SO much!