Construct triangle pqr pq=5.5cm we=4cm angle pqr= 75°

I assume you can construct at 30° angle (bisect a 60° angle) and a 45° angle. Add them together to get your 75°

so,
draw QP of length 5.5
draw angle Q = 75°
I have no idea what WE is, but I shall assume QR
With Q as center, draw a circle of radius 4
R is where the constructed angle's ray from Q intersects the circle.