SOLUTION: Please help me with the problem below: Two hikers come to a fork in a road. One walks down one straight branch at 3 mph and the other walks down the other straight branch at 3.5

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Question 982743: Please help me with the problem below:
Two hikers come to a fork in a road. One walks down one straight branch at 3 mph and the other walks down the other straight branch at 3.5 mph. If the angle between the branches is 30 degrees find the distance between the two hikers after one hour.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Uniform Rates of Travel, RT=D, and Law of Cosines.




Draw the triangle. The unknown side opposite the 30 degree fork is what you want to solve for. Calling this segment length d,

%283.1%29%5E2%2B%283.5%2A1%29%5E2-2%283%29%283.5%29cos%2830%29=d%5E2
9%2B12.25-21%28sqrt%283%29%2F2%29=d%5E2
d%5E2=21.25-21%28sqrt%283%29%2F2%29
highlight%28d=sqrt%2821.25-21%28sqrt%283%29%2F2%29%29%29-----simplify or compute.