How to construct a triangle given the base length, altitude and the vertical angle

Draw line AB=100mm the base length
Bisect line AB
At point A, draw the vertical angle{60} to create line CD
At point A along line CD erect a perpendicular that intersects with the bisector of AB at point O.
At point O and using OA or OB as the radius, draw a circle the inscribes the required triangle
With points A and B being the centres draw arcs whose radius = altitude=50mm
Draw a line that is tangential to the arcs
At the points where the line cuts the circumference of the circle are E and F
Join point A to point F and point B to point F
Triangle ABF is the required triangle