SOLUTION: Two drivers leave home at the same time and travel on straight roads that diverge by 70 degrees. One driver travels at an average speed of 83.0 km/h. The other driver travels at an

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Question 451819: Two drivers leave home at the same time and travel on straight roads that diverge by 70 degrees. One driver travels at an average speed of 83.0 km/h. The other driver travels at an average speed of 95.0 km/h. How far apart will the two drivers be after 45 min?
Answer by ankor@dixie-net.com(22740) (Show Source):
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Two drivers leave home at the same time and travel on straight roads that diverge by 70 degrees.
One driver travels at an average speed of 83.0 km/h.
The other driver travels at an average speed of 95.0 km/h.
How far apart will the two drivers be after 45 min?
:
Convert 45 min to .75 hrs
:
Let A = 70 degrees
then
a = distance between the cars after 45 min
b = .75(83) = 62.25 km
c = .75(95) = 71.25 km
:
Use the law of cosines
a^2 = b^2 + c^2 - 2bc*cos(A)
a^2 = 62.25^2 + 71.25^2 - 2(62.25*71.25)*cos(70)
a^2 = 3875.0625 + 5076.5625 - 2(4435.3125)*.34202
a^2 = 8951.625 - 3033.9324
a =
a = 76.92 km apart after 45 min