It is a table that gives the cosines of angles, usually from 0 to 90 degrees in steps on 0.1 degree. These were used extensively for trigonometric calculations before the advent of computers.
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The law of cosines with a right angle is just the pythagorean theorem. The cosine of 90 degrees is 0. That is why the hypotenuse squared is equal to the sum of both of the legs squared
The law of cosines can be written in one form as: c2 = a2 + b2 - 2abCos C. Without 3 of the 4 variables being given, there is no way to answer this question.
Yes
Trigonometry mainly but also geometry, algebra.
It follows from the cyclical symmetry of the cosine rule.