Answer:
Step-by-step explanation:
We have plane 1 flying SW for 4 hours at a rate of 415 mph. The distance he covers using the d = rt formula for distance, is 415(4) = 160 miles.
We also have plane 2 flying directly east (along the x-axis) for 4 hours at 327 mph. The distance he covers using the d = rt formula for distance, is 327(4) = 1308 miles. The angle in between them at this point is 135 degrees, and what we need to find is the length of the vector connecting the 2 planes. IF this was right triangle trig that distance would be the hypotenuse and we could solve for it using Pythagorean's Theorem. BUT it is NOT a right triangle, so we have to find some other means with which to solve for that length. We will use the Law of Cosines to do this.
[tex]?^2=1660^2+1308^2-2(1660)(1308)cos(135)[/tex] which simplifies a bit to
[tex]?^2=2755600+1712864-(-3070653.624)[/tex]
If you add all of that together, you'll get
[tex]?^2=7537117.624[/tex] and you'll take the square root of that to get that the distance between the 2 planes after 4 hours is
2745 miles
