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The Wonder and Amusement of Triangles - Part Five : the Law of Tangents
To begin with
This proof is quite short, sharp and shocking, so not much is required for it. The Law of Tangents is the one we can use to find how two of the sides of a triangle are related to the two angles opposite each of them. To see what I mean, take note of the Illustration below.
The Proof, from Wikipedia™, by Chris Lilly on Paintbox™
As much as some of this Hub contains certain Mathematical knowledge accessible in the public domain, and not subject to any Copyright, other information has been drawn from textbooks which themselves are Copyright, but only in the sense of how they deliver the information which itself is shared and sometimes ancient Mathematical knowledge. Other information can be found on Wikipedia ( Copyright 2014, the Wikimedia Foundation ), which is a good source of information, and part of an article thereon concerning the Law of Tangents has been paraphrased into the second Illustration used in the Hub.
All of the illustrations in this particular Hub may be my own, but with information from Textbooks, and as mentioned, Wikipedia™, and have primarily been done using Microsoft™ Paintbox, edited from illustrations done using Microsoft™ Word. Any quote or part of this material which seems to belong to any other author should be treated as such, and I claim no ownership of anything I did not myself invent or discover, nor of any obvious copyright, trade mark, or registered trade mark.
The Adventure continues in the next Hub, about something I call Rotactional Angles, so if You are curious, have a look when it is finally done.
If You want to know more, then do not hesitate to take a good look at the other Hubs, The Maths They Never Taught Us - Part One, The Maths They Never Taught Us - Part Two , The Maths They Never Taught Us - Part Three, The Very Next Step - Squares and the Power of Two , And then there were Three - a Study on Cubes, Moving on to Higher Powers - a First look at Exponents, The Power of Many More - more on the Use of Exponents, Mathematics - the Science of Patterns , More on the Patterns of Maths , Mathematics of Cricket , The Shape of Things to Come , Trigonometry to begin with , Pythagorean Theorem and Triplets, Things to do with Shapes, Pyramids - How to find their Height and Volume, How to find the Area of Regular Polygons, The Wonder and Amusement of Triangles - Part One, The Wonder and Amusement of Triangles - Part Two, the Law of Missing Lengths, The Wonder and Amusement of Triangles – Part Three : the Sine Rule, and The Wonder and Amusement of Triangles - Part Four : the Cosine Rule.
Also, feel free to check out my non Maths Hubs :
There will also be many More to come on a wide variety of Subjects.
Just take a good look at it, and note how interesting it all is, then see if you can come up with anything else along the same lines. As usual, I would appreciate any comments, feedback and suggestions which would be given due credit, or indeed have a go and publishing Your ideas Yourselves, but firstly, by all means, add Your comments - it's a free Country.