Question

The locations, given in polar coordinates, for two planes approaching an airport are (4 mi, 12º) and (3 mi, 73º). Find the distance between the two planes.

Answer 1

To get the distance between the two planes we use the cosine rule;
c^2=a^2+b^2-2abCosC
thus;'
a=4 miles
b=3 miles
C=73-12=61
thus
c^2=4^2+3^2-2*3*4Cos 61
c^2=16+9-24cos61
c^2=25-24cos61
c^2=13.3646
c=sqrt13.3646
c=3.66 miles
They two planes are 3.66 miles apart