Two planes takeoff from an airport at some time one travelin

Two planes take-off from an airport at some time, one traveling at 450 mph and the other traveling at 500 mph, and their travel directions make an angle of 80 degree. After 2 hours, how far apart art the planes?

Solution

Distance travelled by one = a = 450*2 = 900 mi

Distance travelled by other = b = 500*2 = 1000 mi

Angle C = 80

Now law of cosines,

c = sqrt[a^2 + b^2 - 2ab*cosC] = sqrt[900^2 + 1000^2 - 2*900*1000*cos80] = 1223.7 mi