Which Cosine Rule?
Most recent answer: 01/29/2015
- samuel (age 25)
Nigeria
Rewriting your equations (sorry that the question part doesn't acept formatting) you're wondering which of these two rules is right:
x2=y2+z2+2yzcos(θ) or x2=y2+z2-2yzcos(θ).
The first equation is used in when x, y and z are vectors of lengths x, y and z , x=y+z and θ is the angle between y and z. You draw vector addition by putting the vectors end-to-end. If y and z are the same length and point the same way, then the length of x is 2y=2z.
The second equation is used in when y and z are the lengths of two sides of a triangle, x is the length of the other side, and θ is the angle between the y and z sides. This is just like the vector equation above except that here x=y-z. If y and z are the same length and point the same way, then the length of x is zero.
Sketch the pictures and it will become clear!
Mike W.
(published on 01/29/2015)