Two forces act on the screw eye

Two forces act on the screw eye. If F_1 = 400N and F_2= 600N, determine the angle θ(0^0\leq \theta \leq180^0) between them, so that the resultant force has a magnitude of F_R = 800 N.

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

To find the solution to this problem, we will first draw the vector components as follows.

Now, we will draw the vectors tail to tail as follows.

Now, we can use the law of cosines to figure out \theta. (Forgot the law of cosines?)

We will isolate for \theta step by step.

800^2=400^2+600^2-2(400)(600)\cos(180^0-\theta)

cos(180^0-\theta)=-0.25

180^0-\theta=104.48

\theta=75.52^0

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-21.