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

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Constructing an Isosceles Triangle

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.

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Constructing an Isosceles Triangle

Draw an isosceles triangle with a base of 8 units and two equal sides measuring 5 units each

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Question 3 - Construct an isosceles right-angled triangle ABC