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?

1 Answer
Douglas K.
May 14, 2018

#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"#

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