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 - Constructing an isosceles triangle with base 12 ft. - Mathematics Stack Exchange

An isosceles triangle has a base of 12 cm with equal sides of 20 cm each. How do you determine the area of this triangle accurate to the nearest square centimeter?

How to draw an isosceles triangle knowing the length of its sides

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Draw an Isosceles Triangle with Base 5 Cm and Height 4 Cm. Draw a Triangle Similar to the Triangle Drawn Whose Sides Are 2 3 Times the Sides of the Triangle. - Geometry Mathematics 2

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Constructing an Isosceles Triangle

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Folding an isosceles triangle to prove its two base angles are equal

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geometry - Calculate third point of isosceles triangle given two points and distance - Mathematics Stack Exchange