Which of the following is a key element in the proof of the law of cosines?
a. the triangle inequality theorem
b. angle a+ angle b+ angle=180
c. a=1/2b*h
d. d=square root of (x^2+x^1)+(y^2-y^1)^2

The correct answer is:

D) d=√((x+x¹)+(y²-y¹)² )

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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step-by-step explanation: