The locations of 2 planes approaching an airport in polar co

The locations of 2 planes approaching an airport in polar coordinates (12mi, 50 degrees) and (15mi, 125 degrees). What is the distance between the planes??

Please help, thank you so much.

Solution

( 12 mi , 50 degrees) and ( 15mi , 125 degrees )

angle between two coordinates = 125 - 50 = 75 degrees

distance between two coordinates is given by the formula

c^2 = a^2 + b^2 - 2ab cos C

c^2 = 12^2 + 15^2 - 2(12)(15) cos 75

c^2 = 144 + 225 - 93.17

c = 16.608 miles