Algebra and Trigonometry, 5th Edition

Chapter 8 Summary and Review Study Guide

KEY TERMS AND CONCEPTS	EXAMPLES
Section 8.1: THE LAW OF SINES
Solving a Triangle To solve a triangle means to find the lengths of all its sides and the measures of all its angles. Any triangle, right or oblique, can be solved if at least one side and any other two measures are known. We cannot solve a triangle when only the three angle measures are given. The Law of Sines In any $\text{Δ}ABC$, $${\displaystyle \frac{a}{\sin A}}={\displaystyle \frac{b}{\sin B}}={\displaystyle \frac{c}{\sin C}}.$$ The law of sines is used to solve triangles given a side and two angles (AAS and ASA) or given two sides and an angle opposite one of them (SSA). In the SSA situation, there are three possibilities: no solution, one solution, or two solutions.	Solve $\text{Δ}RST,\text{ if }r=47.6,S=123.5°,\text{ and }T=31.4°$.