Wrong!
45 degrees is too steep. The foundations for the pool need to be behind a line drawn from the toe of the slope equal to the long term stable slope plus a factor of safety.
For a slope that is composed of granular soil with say a friction angle of 35 degrees the slope angle should be equal to:
Tan(B)=Tan(35)/1.5
where B is the angle of the line drawn from the toe of the slope.
There are other approaches but the 45 degree line that you imagine is what geotechnical engineers generally assume that the vertical stresses shed at beneath a footing. It has nothing to do with the stability of the slope.
If you have groundwater discharge or clayey soils then a more detailed analysis is required.