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8. Construct a Triangle Given the Lengths of Two Sides and the Length of the Altitude to One of Them

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This Demonstration shows a construction of a triangle given the lengths and of the sides and and the length of the altitude from to .

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Construction

Draw a line segment of length , and let be the midpoint of .

Step 1: Draw the circle with center and radius . Measure out a point on at distance from .

Step 2: Extend to such that .

Verification

Since is a right-angled triangle and by construction, is the altitude to and has length .

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Contributed by: Izidor Hafner (August 2017)
Open content licensed under CC BY-NC-SA

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Reference

[1] D. S. Modic, Triangles, Constructions, Algebraic Solutions (in Slovenian), Ljubljana: Math Publishers, 2009 pp. 44.

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