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# Short Response Two groups start hiking from the same camp. Group A hikes 6.5 miles due west and then hikes 4 miles in the direction N 35 $^{\circ}$ W. Group B hikes 6.5 miles due east and then hikes 4 miles in the direction $N 45^{\circ} \mathrm{E}$ At this point, which group is closer to the camp? Explain.(IMAGE CANNOT COPY)

## Group $A$ is closer to the camp.

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We have two groups of campers leaving the same group. Same camp Group A leaves camp and travels 6.5 miles west at the same time. Group B leaves camp and travels 6.5 miles east, so the first part of their trip both groups are the same distance from Camp Group A, then turns north and goes forth four miles. But they don't just go north four miles. Otherwise, that would be a 90 degree angle. They go north, four miles and 35 degrees west, so that means they are traveling this path for four miles, and you've got a total of 100 25 degrees from the original path of going West Group two. Again, they go four miles north, but they don't just go north. That again would be 90 degrees. They also go 45 my 45 degrees east, so that would put them at 135 degrees from their original path of going east. So the question is, is which group is closer to camp? Well, if I completed two triangles of the triangle going from their original camp to their ending position, we could use Hitch hinge there. Um, that states the side opposite the smaller angle is gonna be the shortest length. The side opposite of the longest angle is gonna be the longer length. So which group is closer? Group A.

University of Oklahoma

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