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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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45°–45°–90° Triangles

Note: Problems 3.1–3.3 refer to the diagram below, featuring right triangle XYZ, in which XY = YZ.

3.1    Given in the triangle, explain why both acute angles measure 45°.

All triangles contain three angles whose measures have a sum of 180° = π radians. Apply this geometric theorem to the given triangle by adding the measures of angles X, Y, and Z, and setting the sum equal to 180°.

In this diagram, angle Y is a right angle, ...

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