Question 548679
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=((Cos(75) + Cos(55)*Cos(50))/(1-Cos(50)^2))*JR}}} (4)

OR

{{{JK=((Cos(75) + Cos(55)*Cos(50))/(Sin(50)^2))*JR}}} (5)

OR for JR:

{{{JR= (Sin(50)^2/(Cos(75) + Cos(55)*Cos(50)))*JK}}} (6)


in the same way substituting JR in JK formulas (2) in (1) will have:

{{{JK=((Cos(50)+Cos(55)*Cos(75))/(Sin(75)^2))*KR}}} (7)

OR

{{{KR=(Sin(75)^2/(Cos(50)+Cos(55)*Cos(75)))*JK}}} (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.