This tool can be used to explore the relationship between the Pythagorean theorem and the Law of Cosines. By considering the "defects" that occur when the angle is obtuse or acute instead of right, the user can develop an intuitive understanding of the Law of Cosines. The geometric interpretation shown below highlights that the Pythagorean theorem is a special case of the Law of Cosines.
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Adjust the Angle Slider to change the measure of Angle C. Click the Reset to Right Angle button to set the measure of angle C to 90°.
Points A and B can be adjusted to change the size and shape of the triangle and squares. The areas of the squares are automatically recalculated.
Click the Show Defect buttons to reveal the irregularity that occurs when the triangle is not a right triangle. Click the Hide Defects button to remove these regions.
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