geometry - How to construct an isosceles triangle given the base

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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

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Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1(1/2) times the corresponding sides of the isosceles triangle.

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