Airport control tower measures the distance to one plane taken off at 500m and distance to second plane coming for a landing at 1050m. If the angle between the lines of observation on radar screen is 86 degrees> how far apart are the two planes?

How about just using the cosine law?

let the distance be x

x^2 = 500^2 + 1050^2 - 2(500)(1050)cos 86°