Problema Solution
Two planes leave an airport at the same time. One plane is flying on a heading of 55 degrees at 30mph and the other plane heading on 352 degrees at 280mph. what is the distance separating them after 2 hours?
Answer provided by our tutors
Using The Law of Cosines we can find the distance as one of the sides of a triangle whose 2 other sides are the distances that each of the planes crossed in 2 hours, and the angle opposite this distance is (360 - 352) + 55 = 63 degrees (make a drawing).
d = the distance between the planes after 2 hours
Using the equation distance = speed*time we have:
d1 = 2*30 = 60 mph the distance that the first plane has crossed
d2 = 2*280 = 560 mi the distance that the second plane has crossed
d^2 = d1^2 + d2^2 - 2*d1*d2*cos(63)
d^2 = 60^2 + 560^2 - 2*60*560*cos(63)
........
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d = 535.44 mi
The distance separating the planes after 2 hours is 535.44 mi.