# Triangles

**URL:** https://boards.straightdope.com/t/triangles/579213
**Category:** Factual Questions
**Created:** [April 21, 2011, 12:07pm UTC](https://boards.straightdope.com/t/triangles/579213 "2011-04-21T12:07:26Z")
**Posts on this page:** 3
**Page:** 2

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### Author: ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)
#### Post date: [April 29, 2011, 12:53am UTC](https://boards.straightdope.com/t/triangles/579213/21 "2011-04-29T00:53:11Z")

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I explained how I derived the formula in post 15.

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### Author: ![dallen2408](https://avatars.discourse-cdn.com/v4/letter/d/7bcc69/32.png) [@dallen2408](https://boards.straightdope.com/u/dallen2408)
#### Post date: [April 29, 2011, 11:56am UTC](https://boards.straightdope.com/t/triangles/579213/22 "2011-04-29T11:56:45Z")

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Thanks for reminding me. Could you fill in the missing steps that you indicated you left out?

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<div class="post-metadata">

### Author: ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)
#### Post date: [April 29, 2011, 4:48pm UTC](https://boards.straightdope.com/t/triangles/579213/23 "2011-04-29T16:48:17Z")

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a’ = a - x cot(beta) - x cot(gamma) - y csc(gamma) - z csc(beta)  
= a - x (a^2+ c^2 - b^2)/(4A) - x (a^2+ b^2 - c^2)/(4A) - aby/(2A) - acz/(2A)  
= a - a^2 x/(2A) - aby/(2A) - acz/(2A)  
= a(A - ax/2 - by/2 - cz/2)/A

So…

A’ = A (a’/a)^2  
= A ((A - ax/2 - by/2 - cz/)/A)^2)  
= ((A - ax/2 - by/2 - cz/2)^2)/A

Keep in mind that I am posting from my phone so you may need to correct some typos here and there.

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