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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

Triangles and its all properties

Isosceles triangle

geometry - How to construct an isosceles triangle given the base angle and height to one side? - Mathematics Stack Exchange

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Draw an isosceles triangle with each of equal sides of length 3 cm and the angle

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