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.