SOLUTION: Thank you in advance for your help! I was really struggling with this problem: Two planes take off from the same airport at the same time using different runways. One plane trav

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Question 1130256: Thank you in advance for your help! I was really struggling with this problem:
Two planes take off from the same airport at the same time using different runways. One plane travels on a bearing S 15 degrees W at 250 miles per hour. The other plane travels on a bearing
N 75 degrees E at 300 miles per hour. How far are the planes from each other 2 hours after takeoff?
Answer: The distance is approximately ___ miles ( round to the nearest mile as needed)
THANK YOU AGAIN FOR YOUR HELP!!
Found 2 solutions by Theo, josmiceli:
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
my diagram is shown below.
once you have figured out how to draw the diagram, the rest is application of the law of cosines for angle C.

that law is:

c^2 = a^2 + b^2 - 2 * a * b * cos(C)

side b is equal to 2 * 250 = 500 miles.
side a is equal to 2 * 300 = 600 miles.

angle ACS is 15 degrees west of south.

angle NCB is 75 degrees east of north.

since angle NCE is 90 degrees, angle BCE is 15 degrees.

angle SCE is 90 degrees.

therefore angle ACB is equal to 15 + 90 + 15 = 120 degrees.

the rest is application of the law of cosines to get c = 954 miles.

that's the distance between the 2 planes after 2 hours.

Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
You can use law of cosines which gives you
opposite side if you have 2 sides and included angle
------------------
Draw the picture. You have 120 degrees between
the flight paths
1st plane;

mi
2nd plane:

mi
----------------------

mi
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check my math. This looks in the ballpark, since
it's a little less than