SOLUTION: this was on my home work jason,kevin,and randy found themselves far apart when they stoped for lunch while working in a field.jason could see kevin,then turn through 75degrees and

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Question 548679: this was on my home work
jason,kevin,and randy found themselves far apart when they stoped for lunch while working in a field.jason could see kevin,then turn through 75degrees and see randy.kevin could see randy,the turn 50 degrees and see jason.randy could see jason,then turn through 55 degree and see kevin.which two were farthest apart ?
a: kevin and randy
B: jason and kevin
C:randy and jason
D: kevin and randy were the same distance apart as randy and jason

Found 2 solutions by stanbon, skarout:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
this was on my home work
jason,kevin,and randy found themselves far apart when they stoped for lunch while working in a field.jason could see kevin,then turn through 75degrees and see randy.kevin could see randy,the turn 50 degrees and see jason.randy could see jason,then turn through 55 degree and see kevin.which two were farthest apart ?
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Draw the picture.
The side opposite the largest angle is the longest side.
Jason is at the vertex of the largest angle.
Kevin and randy are opposite the largesst angle
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Ans: a
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Cheers,
Stan H.
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a: kevin and randy
B: jason and kevin
C:randy and jason
D: kevin and randy were the same distance apart as randy and jason

Answer by skarout(1) About Me  (Show Source):
You can put this solution on YOUR website!
Let us give a name for each point where each person stand:
J for Jason / K for Kevin / R for Randy.
Let we draw the triangle where Jason-Kevin ^ Jason-Randi angle 75deg
so JK^JR = 75deg
same for:
KJ^KR = 50deg
RK^RJ = 55 deg
having this triangle RJK, draw perpenducular lines from each point to each opposit side, it will divide each side to two segment.
so
JK = JR*Cos(75) + KR*Cos(50) (1)
JR = JK*cos(75) + KR*Cos(55) (2)
KR = JK*Cos(50) + JR*Cos(55) (3)
substitute for KR in JK formulas (3) in (1):
JK = JR*Cos(75) + [JK*Cos(50) + JR*Cos(55)]*Cos(50)
JK = JR*Cos(75) + JK*Cos(50)*Cos(50) + JR*Cos(55)*Cos(50)
this will lead to:
JK=%28%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%2F%281-Cos%2850%29%5E2%29%29%2AJR (4)
OR
JK=%28%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%2F%28Sin%2850%29%5E2%29%29%2AJR (5)
OR for JR:
JR=+%28Sin%2850%29%5E2%2F%28Cos%2875%29+%2B+Cos%2855%29%2ACos%2850%29%29%29%2AJK (6)

in the same way substituting JR in JK formulas (2) in (1) will have:
JK=%28%28Cos%2850%29%2BCos%2855%29%2ACos%2875%29%29%2F%28Sin%2875%29%5E2%29%29%2AKR (7)
OR
KR=%28Sin%2875%29%5E2%2F%28Cos%2850%29%2BCos%2855%29%2ACos%2875%29%29%29%2AJK (8)

Calculate the result for (6) and (8):
formula (6) will give: JR = 0.93516 * JK this means that: JR < JK
and (8) will give: KR = 1.17917 * JK this means that: JK < KR
so we have JR < JK < KR
so farthest two points are KR
this means that Kaven and Randy are the farthest apart.
so answer is "a"
thanks.