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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