What are the equations for Law of Sines and Law of Cosines? Will mark as BRAINLIEST if answer you give me is right. :)

Law of Sines: ,

where a is the angle of opposite of side A and b is the angle opposite of side B

Extend law of sines to all three sides and angles of the triangle to get:

,

where a is the angle of opposite of side A, b is the angle opposite of side B, and c is the angle opposite of side C

Law of Cosines: OR ,

where C is the unknown side, A and B are the two known sides, and angle c is the angle opposite of the unknown side

(algebraic manipulation will get you from equation 1 to 2 by taking the square root of both sides)

what many people tend to get confused for the law of cosines is that they label sides of a triangle ABC regardless of whether or not the side value is unknown or known. If you do this, just make sure that the unknown side is always isolated, not whatever the value side C of the triangle you labeled is.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer