Finding Angles from Three Sides (SSS)

Trigonometry · Axiom Academy

EXAMPLE Finding Angles from Three Sides (SSS) Learn to find all angles of a triangle when given three sides using the Law of Cosines strategically. Excellent work! You've successfully solved an SSS triangle problem. Here's what we learned: Strategic Choice: Start with the angle opposite the shortest side. This often gives the largest angle and simplifies calculations. Law of Cosines: Use cos(C) = (a² + b² - c²) / (2ab) to find angles when all three sides are known. Systematic Approach: Find two angles using Law of Cosines, then use the angle sum property (A + B + C = 180°) for the third angle. Alternative Method: After finding one angle with Law of Cosines, you can use Law of Sines for the remaining angles (often faster!). Verification: Always check that your three angles sum to 180° to verify your answer. The SSS case is one of the most reliable methods for solving triangles because you're given complete information. This technique is essential in surveying, navigation, and engineering applications!

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