SOLUTION: Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range of 100 yards. From their starting point, they head off at an angle of 109°10' of

Algebra ->  Trigonometry-basics -> SOLUTION: Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range of 100 yards. From their starting point, they head off at an angle of 109°10' of       Log On


   

Question 1205892: Two hikers are wandering through heavy woods with walkie talkies. The walkie talkies have a range of 100 yards. From their starting point, they head off at an angle of 109°10' of each other. Hiker 1 walks 0.24 miles per hour, hiker 2 walks 0.17 miles per hour. If each continues to go straight, how long will it be before they can no longer communicate?

Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52913) About Me  (Show Source):
You can put this solution on YOUR website!
.

Convert miles per hour to yards per hour.

After that, apply the law of cosine formula.


Happy calculations (!)


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Notice that cosine law equation in the post by @josgarithmetic is INCORRECT.

Do not use it.

The correct form of this equation is 
    %280.24x%29%5E2%2B%280.17x%29%5E2-2%2A0.24x%2A0.17x%2Acos%28109%2610%2F60%29 = 0.0561818%5E2.

Use it to find the time x.



Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
100%2Ayards%2A3%28feet%2Fyard%29%281%2F5280%29%28miles%2Ffeet%29

0.0561818 mile

The hikers walk for x number of hours, according to given separation angle from starting point.
%280.24x%29%5E2%2B%280.17x%29%5E2-2%2A0.24%2A0.17%2Acos%28109%2610%2F60%29=0.0561818%5E2
Simplify and solve for x.