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en:proof-of-the-law-of-cosines [2017/04/12 13:15] federico [Proof] |
en:proof-of-the-law-of-cosines [2017/07/14 10:36] federico |
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===== Proof ===== | ===== Proof ===== | ||
- | If divide the triangle into 2 right angle triangles: | + | Divide the triangle into 2 right angle triangles: |
- | {{:en:law-of-cosines2-fs8.png?nolink&200|}} | + | {{:en:law-of-cosines2-fs8.png?nolink|}} |
Using trigonometry, the sides of the green triangle are | Using trigonometry, the sides of the green triangle are | ||
Line 15: | Line 15: | ||
* (b sin θ) | * (b sin θ) | ||
* (c - b cos(θ)) | * (c - b cos(θ)) | ||
+ | |||
+ | {{:en:law-of-cosines3-fs8.png?nolink|}} | ||
Using the Pythagorean Theorem: | Using the Pythagorean Theorem: |