SOLUTION: Two airplanes leave an airport at the same time. The heading of the first is 120 degrees and the heading of the second is 320 degrees. If the airplanes travel at the rates of 700 m
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Question 156803: Two airplanes leave an airport at the same time. The heading of the first is 120 degrees and the heading of the second is 320 degrees. If the airplanes travel at the rates of 700 mph and 600 mph respectively, how far apart are they after an hour?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two airplanes leave an airport at the same time. The heading of the first is
120 degrees and the heading of the second is 320 degrees. If the airplanes
travel at the rates of 700 mph and 600 mph respectively, how far apart are
they after an hour?
:
Draw a diagram of this. A triangle with legs of 700 and 600 enclosing angle A
:
side a = distance apart (opposite angle A)
and
side b = 700
side c = 600
;
Find Angle A: (360-320) + 120 = 160 degrees
;
Use the law of cosines:
a^2 = b^2 + c^2 - 2(b*c)cos(A)
:
a^2 = 700^2 + 600^2 - 2(700*600)Cos(160)
:
a^2 = 490000 = 360000 - 2(420000)* -.939692
:
a^2 = 850000 - (840000*.-939692)
:
a^2 = 850000 -(-789342)
:
a^2 = 850000 + 789342
:
a =
:
a = 1280.4 miles apart in 1 hr
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