Find the diameter of a circle with a central angle of 110 degrees and a segment measuring 8 ft.

(To the extent possible use standard angles to simplify your responses. When necessary express your answers using the functions sin, cos, sin−1, cos−1. If there is no solution enter IMPOSSIBLE.)

Draw the diagram. You can see that

4/r = sin55°
so d = 2r = 8/sin55°