1. The problem statement, all variables and given/known data I am a new physics student am having trouble with a sample problem from the book. I have the answer (below) but I don't not understand how they are finding that number. I have been trying to make sense of it using the pythagorean theorem and Law of Cosines but I just cannot break it. I have copied and pasted the problem below and included the graphic from the book. Please help. In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) , 2.0 km due east (directly toward the east); (b), 2.0 km 30° north of east (at an angle of 30° toward the north from due east); (c), 1.0 km due west. Alternatively, you may substitute either -b for b or -c for c. What is the greatest distance you can be from base camp at the end of the third displacement? Reasoning: Using a convenient scale, we draw vectors a, b, c, -b, and -c as in Fig. 3-7a. We then mentally slide the vectors over the page, connecting three of them at a time in head-to-tail arrangements to find their vector sum d. The tail of the first vector represents base camp. The head of the third vector represents the point at which you stop. The vector sum d extends from the tail of the first vector to the head of the third vector. Its magnitude d is your distance from base camp. 2. Relevant equations Also, I don't understand what happens to c for it to become -c. Does that mean instead of 1, it is -1? I have been fumbling around with the Law of Cosines because i think it is related to finding the answer to this problem, but I'm not clear on how to use it. c2=a2+b2-2abcosC b2=a2+c2-2accosC a2=b2+c2-2bccosC 3. The attempt at a solution D=4.8, but I have not been successful at reverse engineering.