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The best and most correct answer among the choices provided by the question is the fourth choice "d=square root of (x^2+x^1)+(y^2-y^1)^2"
The law of cosines for calculating one side of a triangle when the angle opposite and the other two sides are known. Can be used in conjunction with the law of sines to find all sides and angles. 

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The correct answer is:

D) d=√((x+x¹)+(y²-y¹)²
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Explanation:

The distance formula is a key component to the proof of the law of cosines.

First we define sin θ = y/b and cos θ = x/b, using the standard law of cosines diagram.

We then use the distance formula, replacing the second y coordinate with 0 and the second x coordinate with a.

We then substitute our values for sin θ and cos θ, square them and simplify.

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