Question

Two forces, A and B, have a resultant C. (In other words A + B = C, as vectors). If A = 5 N, B = 7 N and C = 8 N, what is the angle between A and C?

Answer 1

`angleB = pi/3" rad "(60^@)`

Explanation:

If we change the vectors to lower case and treat them as sides of a triangle, `a = 5, b = 7, and c = 8`, then `angle B` is the angle between sides `a` and `c`; this allows us to use the law of cosines:

`b^2= a^2+c^2-2(a)(c)cos(B)`

`7^2= 5^2+8^2-2(5)(8)cos(B)`

`7^2-5^2-8^2=-2(5)(8)cos(B)`

`cos(B)=(7^2-5^2-8^2)/(-2(5)(8))`

`cos(B)=1/2`

`angleB = pi/3" rad"`