Here is the construction with required traces of construction
Steps followed
1) A line segment AB of length 5.8 cm is drawn
2) Angle BAD =105° is drawn with the help of a ruler and a compass..
3) AC the bisector of angle BAD is drawn.
Now angle CAB = angle CAD=52.5°
4) Angle ABC=angle CAB is drawn.
5)ABC triangle formed becomes required triangle as angle ACB=75° and AB=5.8cm.