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
May 14, 2018

angleB = pi/3" rad "(60^@)B=π3 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 = 8a=5,b=7,andc=8, then angle BB is the angle between sides aa and cc; this allows us to use the law of cosines:

b^2= a^2+c^2-2(a)(c)cos(B)b2=a2+c22(a)(c)cos(B)

7^2= 5^2+8^2-2(5)(8)cos(B)72=52+822(5)(8)cos(B)

7^2-5^2-8^2=-2(5)(8)cos(B)725282=2(5)(8)cos(B)

cos(B)=(7^2-5^2-8^2)/(-2(5)(8))cos(B)=7252822(5)(8)

cos(B)=1/2cos(B)=12

angleB = pi/3" rad"B=π3 rad