How would I convert this equation from polar form to Cartesian/rectangular form? My book gives the answer in the index, but doesn't explain how to get it, and I've been trying multiple ways of solving it.

18

When we have an angle formed from three points on a circle making two chords, so the angle itself is sitting on the circle, the angle is half the arc measure.

If the two chords meet in the middle of the circle, the sum of the arcs enclosed by two opposite (but congruent angles) equals the sum of the angles, so twice either one of them.

In this figure we have the chords meeting outside the circle.  So the two arcs are working against each other, and the included angle, x here, is half the difference of the two arcs,

x = (1/2)(100 - 26) = 74/2 = 37 (degrees)

37

20

Again we have intersecting secants but this time we're concerned with the various lengths.   The theorem says the product of the piece outside the circle times the total segment (to the other side of the triangle) is the same whichever line we use.  Here that means

6(6+x) = 5(5+10)

36 + 6x = 75

6x = 39

x = 13/2

13/2