geometry - How to construct an isosceles triangle given the base

I've got this math exercise. It reads: Construct an isosceles triangle given the base angle and height to one side. How many solutions exist? Why? I made a sketch, but still can't figure out

geometry - Solve for the base of an isosceles triangle - Mathematics Stack Exchange

Question 2 - Construct an isosceles triangle in which the lengths of

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Construct an isosceles triangle ABC with BC =6.2 cm and altitude =4.4 cm.

Construct an isosceles triangle whose base is 6 cm and altitude 4 cm. Then construct another triangle whose sides are `3/4`times the corresponding sides of the isosceles triangle. - Mathematics

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Isosceles triangle