Expert: Sherman D. - 12/31/2007

Question
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? (I need to use either the Law of Sines of the Law of Cosines).

Answer
S = d/t
d = St

c^2 = (.17x)^2 + (.24x)^2 - 2(.17x * .24x)cos(109°10)

since this is talking about miles and not yards per hour, then

100 yrds = 0.05682 miles

so you need something over 0.05682 miles to find your answer.

c = sqrt(.0289x^2 + .0576x^2 - .0816cos(109°10')x^2)
c = xsqrt(.0289 + .0576 - .0816cos(109°10'))

so you need the right side to be more than 100 yards for me to answer your question.

x > 0.05682/sqrt(.0289 + .0576 - .0816cos(109°10'))

x > about .168812318 hours, or 10 minutes

to be more accurate, anything over about 10 minutes 8 seconds.

so anything over about 10 minutes will put the 2 hikers out of range.