Problem 316 | Equilibrium of Concurrent Force System

By Cosine Law
$30^2 = 20^2 + 40^2 - 2(20)(40) \cos \alpha$

$2(20)(40) \cos \alpha = 20^2 + 40^2 - 30^2$

$1600 \cos \alpha = 1100$

$\cos \alpha = 0.6875$

$\alpha = 46.57^\circ$           answer
 

 

$20^2 = 30^2 + 40^2 - 2(30)(40) \cos \theta$

$2(30)(40) \cos \theta = 30^2 + 40^2 - 20^2$

$2400 \cos \theta = 2100$

$\cos \theta = 0.875$

$\theta = 28.96^\circ$           answer