1. A dog sits under the only shade tree in its territory. Suddenly the dog desires to dig a previously buried bone. From the tree the dog goes 13 meters at 22.6° north of east. Not finding the bone there the dog then goes 17 meters at 61.9° north of west. Digging at the second location yields a bone. To go directly from the tree to the bone the dog should have gone what distance in what direction? Answer: 20.4m @ 78.7° N of E

Question

1. A dog sits under the only shade tree in its territory. Suddenly the dog desires to dig a previously buried bone. From the tree the dog goes 13 meters at 22.6° north of east. Not finding the bone there the dog then goes 17 meters at 61.9° north of west. Digging at the second location yields a bone. To go directly from the tree to the bone the dog should have gone what distance in what direction?   Answer: 20.4m @ 78.7° N of E
The answer is given above, but I am confused as to how to get to the answer using the law of cosine and sine. Thanks!

Henry · Answer

Disp. = 13m[22.6o] + 17[118.1o]. Disp. = (13*Cos22.6+17*Cos118.1) + (13*sin22.6+17*sin118.1)i, Disp. = 4 + 20i = 20.4m[78.7o N. of E].