# Q & A: which cosine rule?

Q:
In resultant and equilibriant of forces, why does physics use a plus sign instead of the minus sign in cosine rule.Maths cosine rule: x2= y2+z2-2yzcosx WhilePhysics will useX2= y2+z2+2yzcosx.Please which one is correct and should be used in solving resultant and equilibriant of forces. Thanks
- samuel (age 25)
Nigeria
A:

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 xy and z are vectors of lengths x, y and z , x=y+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)