Square Inscribed on Any Base of a Triangle

Take any triangle ABC.

Problem 1.

Develop a ruler and compass construction for inscribing a square in a triangle with one side along a specified base.

Help? See

Squares Inscribed in a Right Triangle.

Problem 2.

Given the inscribed square as indicated in the drawing, find an expression for

sin terms ofhanda.

This result shows that the length of the side of a square inscribed on a given base of a triangle is

one half the harmonic meanof the altitude to that base and the base.

Another wayto set it up.

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