Answer:
887 mi
Explanation:
You want the distance between two planes that have each traveled 500 miles on courses that are 125° apart.
Law of cosines
The law of cosines can help you find the side c in a triangle when sides a and b are given, along with angle C between them.
c² = a² +b² -2ab·cos(C)
Here, this means ...
c² = 500² +500² -2·500·500·cos(125°) ≈ 786788.2
c = √786788.2 ≈ 887.01
The airplanes are about 887 miles apart.
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Additional comment
The second attachment shows an alternate solution. The distance halfway between the planes will be 500 miles times the sine of half the angle between them. That half-distance is ...
500·sin(62.5°) ≈ 443.5 miles
so the distance between the planes is 887 miles.