Problem 315 | Equilibrium of Concurrent Force System

By Cosine Law
$F^2 = 400^2 + 300^2 - 2(400)(300) \cos 30^\circ$

$F^2 = 42\,153.90 \, \text{ lb}$

$F = 205.31 \, \text{ lb}$           answer
 

 

$400^2 = 300^2 + F^2 - 2(300F) \cos \theta$

$2(300F) \cos \theta = 300^2 + F^2 - 400^2$

$600(205.31) \cos \theta = 300^2 + 42\,153.90 - 400^2$

$123\,186 \cos \theta = -27\,846.1$

$\cos \theta = -0.226\,044\,624\,4$

$\theta = 103.06^\circ$           answer
 

The correct position of F would be as shown below.