**Trigonometric Area Formulas**

SAS, ASA, and AAS triangle area formulas

**12.13** Explain the relationship between the variables *x*, *X*, *y*, *Y*, *z*, and *Z* in the trigonometric formulas for the area of a triangle, and construct a diagram to illustrate your answer.

Many trigonometric formulas, including the trigonometric area formulas for triangles in this chapter and the laws of sines and cosines in Chapter 13, contain multiple instances of the same letter, one lowercase and one uppercase. In these instances, the lowercase letter represents the length of a side of the triangle and the uppercase letter represents the measure of the opposite angle. Corresponding letters (*x* and *X*, or *y* and *Y*, for example) are always opposite each other in the diagram.

Consider ...

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