Question

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

Answer 1

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. 

I hope my answer has come to your help. God bless and have a nice day ahead!

Answer 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.