Finding the Third Side (SAS)

Trigonometry · Axiom Academy

EXAMPLE Finding the Third Side (SAS) Use the Law of Cosines to find the third side when given two sides and the included angle. Excellent work! You've successfully found the third side of a triangle using the Law of Cosines. Here's what we learned: SAS Situation: When you have two sides and the included angle, the Law of Cosines is your go-to formula: c² = a² + b² - 2ab·cos(C) Step-by-Step Approach: Calculate squares first (a² and b²), then compute 2ab, evaluate the cosine, and finally combine everything Calculator Mode: Make sure your calculator is in degree mode when working with angles in degrees! This is a common source of errors Final Step: Don't forget to take the square root at the end to get the side length (not the square of the side length) Rounding: Keep intermediate values to at least 4 decimal places to maintain accuracy, then round your final answer appropriately The Law of Cosines is a powerful extension of the Pythagorean theorem that works for any triangle, not just right triangles. You'll use this formula frequently when dealing with SAS or SSS triangle scenarios!

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