Eric and Heather are each taking a group of campers hiking in the woods. Eric’s group leaves camp and goes 2 miles east, then turns 20° south of east and goes 4 more miles. Heather’s group leaves camp and travels 2miles west, then turns 30° north of west and goes 4 more miles. How many degrees south of east would Eric have needed to turn in order for his group and Heather’s group to be the same distance from camp after the two legs of the hike?
first of all, Eric’s group goes 2 miles east. On the other hand, Heather’s group goes 2 miles to the opposite direction. Angle between this opposite direction is 180°. After that, Eric’s group turns 20° south of east and goes 4 more miles, but Heather’s group turns 30° north of west and goes 4 more miles. Angle between replacement vector is 180°+30°-20°=190°. If Eric is going in order of south is the answer is 190°.