Solution Diagram

Set the current position of the rescue ship as the origin (i.e., point O). The final destination is indicated in the figure as point A. In terms of Cartesian coordinates, x = 90 miles and y = 78 miles.

To convert the Cartesian coordinates to polar coordinates, the radial coordinates can be obtained through the Pythagorean theorem:

     r² = x² + y²
         = (90)² + (78)²
            = 14,184

which gives r = 119.1 miles.

The angle coordinates can be determined via trigonometry relation:

     tanθ = y/x = 78/90
     θ = 40.91^o = 0.7141 radians

Hence, in terms of the polar coordinates, the final destination is 119.1 miles in the radial-direction and 40.91^o (or 0.7141 radians) in the θ-direction.