s2.tex

To obtain the resultant force, the projection of the resultant on the vertical and horizontal axes is determined as the sum of the projections of the four forces onto the respective axes,
\begin{align*}
	R_H	&=	F_1 \cos\ang{30} - F_2\sin\ang{20} + F_4 \cos\ang{15}\\
		&=	\SI{199.1}{\N}	\,,\\
	R_V	&=	F_1 \sin\ang{30} +F_2 \cos\ang{20}-F_3 -F_4\sin\ang{15}\\
		&=	\SI{14.3}{\N} \, .
\end{align*}
The angle with the horizontal then follows from
\begin{align*}
	\frac{R_V}{R_H}	&=	\frac{R\sin\alpha}{R\cos\alpha}\\
					&=	\tan\alpha \\
					&=0.0718\, .
\end{align*}
Hence, $\alpha=\ang{4.1}$. The magnitude of the resultant follows from,
\begin{align*}
	|R|	&=\sqrt{R_H^2+R_V^2}\\
			&=	\SI{199.6}{\N}
\end{align*}
\clearpage