Engineering Mechanics: Statics & Dynamics (14th Edition)

$F=917lb$ $\theta=31.8^{\circ}$
We are asked to determine the magnitude of $F$ and its direction, $\theta$ Given that the force on member AB is 650lb and the force of member BC is 500lb, we can apply the law of cosines to find the magnitude of $F$. $c=\sqrt{a^2+b^2-2*a*b*\cos(C)}$ $c=\sqrt{500^2+650^2-2*500*650*\cos(105^{\circ})}$ $c=917$ $F=917lb$ Using this result, we can apply the law of sines to find the$\theta$ $\sin\theta / 500 = \sin 105^{\circ} / 917$ Solving for $\theta$, we obtain: $\theta=31.8^{\circ}$