does anyone know how I could possibly extrude cut that projected curve triangle?
If you want the extrude-cut perpendicular to Plane4, extrude it through all from that using the initial sketch.
You cannot Extrude-cut from a curved surface. The Projected curve is also not a true triangle because its 'hypoteneuse' and one leg are arcs along the curved surface, not lines.
You can create a Lofted Cut from the projected curve, and to do so I would create an equivalent 3D sketch on bottom surface of the body to create the two sketches which the lofted cut will connect, and use the near corner edge in view as its guide curve. I am uncertain if this is the best solution, so I offer a simpler alternative.
You can select the three endpoints of the Projected Curve sketch to create a new reference Plane. Sketch an actual triangle with same endpoints on the new plane. Extrude cut "through all-both" in the direction of the near corner edge in your view.
Is your goal here to cut normal to a plane with that profile or to cut normal to the face itself (a variable cut direction depending on where you are on that face)?
Instead of use projected curve better to use a split line.
After that create a zero offset face and use it to thicken cut.
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