Question

How do you use the law of cosines if you are given x = 12.37, y=10, z=15?

Answer 1

By the Law of Cosines:
`color(white)("XXXX")` `x^2= y^2+z^2- 2yzCos(X)`
`color(white)("XXXX")`or
`color(white)("XXXX")` `Cos(X) = (y^2+z^2-x^2)/(2yz)`

Therefore
`color(white)("XXXX")` `X= Arccos((y^2+z^2-x^2)/(2yz))`

Plugging the given values for `x,y, and z` we can calculate the angles `X, Y, and Z`

(I used `a, b, and c` instead of `x, y, and z` when I set up a spreadsheet to do the calculations. Sorry about that).