How to Derive Heron's Formula

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In this video, we will learn how to derive Heron's formula, which is a formula for finding the area of a triangle from the lengths of its three sides. This formula is a direct application of the Law of Cosines.

Chapters:

00:00 Introduction
00:03 Area Formula
00:42 Step 1: Square both sides
01:22 Step 2: Use the Pythagorean Identity to substitute
01:57 Step 3: Factor using the difference of squares
02:36 Step 4: Solve for cos C
04:49 Step 5: Find 1 + cos C
07:46 Step 6: Find 1 - cos C
12:37 Step 7: Substitutions
13:44 Step 8: Simplify
14:27 Step 9: Rewrite
15:29 Step 10: Semiperimeter substitutions
17:41 Step 11: Finding Heron's Formula

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