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Law of cosines
A caveman from 10,000 BCal-Kashi was the 1st to provide an explicit statement of the law of cosines in a form suitable for triangulation
D. The Pythagorean Theorem
The "vector triangle" illustrates the "dot product" of two vectors, represented as sides of a triangle and the enclosed angle. This can be calculated using the law of cosines. (see link)
We use the law of Cosines to be able to find : 1. The measure of the third side, when the measure of two sides and the included angle of a triangle ABC are known. 2. The measure of any angle, when the measure of the three sides of a triangle ABC are known.
Use the law of cosines (look them up on wikipedia).
If it's a right triangle, use pythagorean's theorem (a2+b2=c2) to solve it. = If it's an oblique triangle, use the law of sines or cosines (see related link)
Yes, absolutely
Law of sines or cosines SinA/a=SinB/b=SinC/c
It's impossible if you don't have any side measures. If you have a right triangle, and angle, and a side, you can use any of the trig functions to find the side. SOH CAH TOA. If you have two sides an an angle sides you can use the law of cosines, which is a2 = (b)2(c)2-2(b)(c)cos(A), or the law of sines, which is sin(A)/a = sin(B)/b The lower cased letters in the equation represent side measures of the corresponding angle measures, which are the upper cased letters.
When none of the angles are known, and using Pythagoras, the triangle is known not to be right angled.
Having sufficient angles or sides one can use either, The Law of Sines, or, The Law of Cosines. Google them.