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27a. Construct a Triangle Given a Side, the Length of the Altitude to It and the Opposite Angle

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This Demonstration constructs a triangle given the length of the base , the angle at and the length of the altitude from to the base.

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Construction

1. Draw a line segment of length .

2. Draw the point so that the angle equals and . Draw the circle with center through and .

3. Draw a line parallel to at distance . The third point of the triangle is the intersection of and .

Verification

The angle at is , since the central angle that subtends equals .

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

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Details

This construction was taken from [1].

Reference

[1] G. Polya, How to Solve It: A New Aspect of Mathematical Method, 2nd ed., Princeton, NJ: Princeton University Press, 1957.

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