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

There is more than one way to do this, but one easy way would be to convert them back in to rectangular coordinates. So convert both coordinates to rectangular form, and then find the distance between the two coordinates in the regular xy plane.

\[( r,\theta)=(r \cos(\theta),r \sin(\theta)) \implies (4 ,12°)=(4 \cos(12), 4 \sin(12)) \approx (3.913,0.832)\]\[(3,73°)=(3 \cos(73), 3 \sin(73)) \approx (0.877,2.869)\] Now find the distance between these two points, i.e the length of the line segment that connects these two points on the cartesian plane. Can you do that?

@essalytee

Answer 2

using the distance formula?

Answer 3

Exactly. The distance between two points.