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  1. An airport control tower measures the distance to one plane, that has just taken off, to be \(500 \thinspace \rm{m}\), and the distance to a second plane, coming in for landing, to be \(1\thinspace 050\thinspace \rm{m}\). If the angle between the lines of observation on the radar screen is \(86^\circ\), how far apart are the two planes? Round your answer to the nearest metre.





  1. Jeff is shooting pucks on an empty net during hockey practice. He is standing to one side of the net. The goal post closest to him is \(23\thinspace \rm{ft}\) away, and the goal post farthest from him is \(26\thinspace \rm{ft}\) away. If the goal posts are \(6\thinspace \rm{ft}\) apart, how many degrees of shooting variance does Jeff have that will result in him getting a goal? Solve using the cosine law, and round your answer to the nearest tenth of a degree.