Two forces act on the screw eye. If F=600 N, determine the magnitude of the resultant force and the angle θ if the resultant force is directed vertically upward.

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

#### Solution:

### Let us first draw the vector components as follows:

### Note that we drew the resultant force vertically upward as stated in the question.

### Now, we can draw the vectors tail to tail.

### \frac{\sin \theta}{600}=\frac{\sin 30^0}{500}

### \theta = 36.87^0

### Now that we have θ, we can figure out \phi.

### \phi=180^0-(30^0+36.87^0) (Remember, all interior angles in a triangle must add up to 180^0)

### \phi=113.13^0

### Now that we have both θ and \phi, we can use the law of sines to figure out F_R.

### \frac{F_R}{\sin 113.13^0}=\frac{500}{\sin 30^0}

### F_R=919.61N

###### This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-23.