It is important to realize that the selected SI Range is not the actual amount of bottom coverage to the left and right (horizontal distance) ...
And while the water depth (23' is this scenario) is figured into the equation (of 40' SI range in this scenario) ... The 40' is Slant Range to the edge of the display (as Gene explained using a 40' long string and arcing this string as one end of the string is attached to the xducer) ...
Slant range is figured using the Pythagorean Theorem ...YUK!! Geometry !!!
In the OP example of 23' water depth with a SI Range setting of 40' ...
Slant Range vs Horizontal Range and Calculating Waypoints
Rickie