Construct a triangle ABC in which BC = 7 cm, <A = 60o and altitude through A is 3.7 cm. How many such triangles are possible? Please tell me the steps of construction.
Description:
1. Draw line BC
2. Draw a parallel to BC with the perpendicular distance of $\displaystyle h_A$
3. Draw the perpendicular bisector of BC
4. Draw in B (or in C) the angle of (90° - <(A)) = 30° , that means <(MBC) = 30°
5. The arm of this angle crosses the perpendicular bisector in M.
6. Draw the circle around M with radius r = MB (or MC)
7. The intersection points of the circle and the parallel to BC are the points A.