Question

Two forces of 27 pounds and 62 pounds act on a body so that the resultant is a force of 76 pounds. Find, to the nearest degree, the angle between the resultant and the larger force.

Answer 1

19 degrees.

Explanation:

Triangle of forces.

We can represent this sytem by a triangle with sides 27, 62 and 76 where the required angle is opposite the smallest side. Then we apply the Law of Cosines:

Cos x = (27^2 - 62^2 - 76^2) / (-2*62*76)

cos x = 0.94344

x = 19.36 degrees.