Subduing My ADD and Learning the Law of Cosines – Maths

Hello Hello! Just an update on my personal life:  I’m working for a software company in Virginia and they haven’t fired me [yet] so I guess that means I get to stay and keep working…

I’m interested in math, science and technology, but being raised by a single mother self-described as ‘hypomanic’ and as a dissident of reality, I had other things to take care of first before I could focus on the *technical* aspects of life, such as attempting to keep my world from spinning out of control…

Hopefully, someone will read this and latch on, provide some input or insight and help feed my intellectual curiosity. I’d very much like to study intellectual property law and help fight the good fight against corporate monopolies in the market of creative enterprise (yes I’m left-wing when it comes to this debate).

This is something (forgive me if this either burdens you or insults your intelligence) I’ve always wanted to get: Trig. I could never hang on and pay attention: cosign, tangent, etc. So anyway, this is exciting! Listen to this – Cosine is just a generalization of Pythagorus’ theorem, which only pertains to RIGHT triangles. So we can find the length of the missing side of a triangle even if that triangle has no 90 degree angle and as long as we have at least one angle inside the triangle. Brilliant! (We can also find the angles inside the triangle if we know the lengths of the sides.)

 

law_of_cosigns

From Wikipedia:

Note:

a  =   alpha;

 =   beta; 

 =   gamma

(These are just symbols to represent the angles as opposed to the lines or segments.)

Law of cosines

In trigonometry, the law of cosines (also known as Al-Kashi law or the cosine formula or cosine rule) is a statement about a general triangle which relates the lengths of its sides to the cosine of one of its angles. Using notation as in Fig. 1, the law of cosines states that

c^2 = a^2 + b^2 - 2ab\cos(\gamma) , \,

or, equivalently:

b^2 = c^2 + a^2 - 2ca\cos(\beta) , \,
a^2 = b^2 + c^2 - 2bc\cos(\alpha) . \,

Note that c is the side opposite of angle γ, and that a and b are the two sides enclosing γ. All three of the identities above say the same thing; they are listed separately only because in solving triangles with three given sides one may apply the identity three times with the roles of the three sides permuted*.

The law of cosines generalizes the Pythagorean theorem, which holds only in right triangles: if the angle γ is a right angle (of measure 90° or \scriptstyle\pi/2 radians), then \scriptstyle\cos(\gamma)\, =\, 0, and thus the law of cosines reduces to

c^2 = a^2 + b^2 \,

which is the Pythagorean theorem.

The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known.

 

*permuted. Changed; these formulas are interchangeable.

P.S. Verily verily the pen is mightier than the sword (but we need both -i.e., pens and swords — or rather, virtual paper and ballistic missiles!).

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