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24b. Construct a Triangle Given the Length of the Altitude to the Base, the Difference of Base Angles and the Sum of the Lengths of the Other Sides

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This Demonstration uses a conchoid to construct a triangle given the difference of the base angles and , the length of the altitude from the base and the sum of the lengths of the legs.

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The conchoid, shown in red, determined by and , intersects the straight line through that forms an angle with the horizontal line through in the points and . The triangle is the solution.

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Contributed by: Nada Razpet, Marko Razpet and Izidor Hafner (October 2017)
Open content licensed under CC BY-NC-SA

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While looking for different solutions to Plemelj's triangle construction problem (given the length of the base , the altitude and the difference ), we came across a more difficult problem: instead of , is given. The problem was solved by Nada Razpet using the conchoid of Nicomedes.

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