a 2 = b 2 + c 2 − 2 ⋅ b ⋅ c ⋅ cos α − − − − − − − − − − − − − − − x 2 = 25 0 2 + 40 0 2 − 2 ⋅ 250 ⋅ 400 ⋅ cos 13 5 0 x 2 = 62 , 500 + 160 , 000 − 200 , 000 ⋅ cos ( 18 0 0 − 4 5 0 ) x 2 = 222 , 500 − 200 , 000 ⋅ ( − cos 4 5 0 ) x 2 = 222 , 500 − 200 , 000 ⋅ 2 2 x 2 = 222 , 500 + 100 , 000 ⋅ 2 x 2 = 2500 ⋅ ( 89 + 40 2 )
x = 50 ⋅ 89 + 40 2 ⇒ x ≈ 603.26 [ mi l es ] A n s . t h e d i s t an ce i s ab o u t 603.26 mi l es
To find the distance between the two planes, we applied the Law of Cosines. After calculating the values, we determined that the distance between the planes is approximately 603.26 miles. The process involved determining the angle between their paths and using the formula to find the distance.
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