Posted by Zahra on Wednesday, March 30, 2011 at 2:16am.
1. Draw the base of the triangle with the given length, call it AB.
2. Draw a line at the prescribed angle to the base, intersection the base at point A. Produce the line above and below the base. The third vertex above the base will be called C, and that below the base will be called C'.
3. Draw a circle, centred at B, radius equal to length of median.
4. From point B, draw a perpendicular to line C'C, cutting it at D.
5. Bisect segment BD and call the mid-point E.
6. Draw a line parallel to C'C through E intersecting the circle at two points M (above AB) and M' (below AB). M and M' are the mid-points of side BC and BC' respectively of the triangles to be constructed.
7. Join BM and produce to intersect C'C at C. Similarly, join BM' and produce to intersect C'C at C'.
8. The required triangles are ABC and ABC'.
Note: The above instructions assume ∠ABC to be acute. If ∠ABC is obtuse, the instructions may vary slightly, but the principle is the same.