26 KN is the resultant of the two forces

26 KN is the resultant of the two forces one of which is shown in the figure. Determine the other force.

26 KN is the resultant of the two forces

Solution:

Let Q be the unknown force which makes an angle θ with horizontal

Given R = 26KN

\begin{equation*}
\theta_1=\tan^{-1}(\frac{12}{5})=67.38^{\circ}\\
\theta_2=\tan^{-1}(\frac{3}{4})=36.87^{\circ}\\
\end{equation*}

\begin{equation*}
\sum Fx = Rx\\
\end{equation*}

10cos36.87 + Qcosθ = 26cos67.38
Qcosθ = 26cos67.38 – 10cos36.87
Qcosθ = 1.99

\begin{equation*}
\sum Fy = Ry
\end{equation*}

10sin36.87 + Qsinθ = 26sin67.38
Qsinθ = 26sin67.38 – 10sin36.87
Qsinθ = 17.99

By Adding,

Qcosθ + Qsinθ = 1.99 + 17.99
Squaring both side
Q = 18.196KN

So the other force will be Q = 18.196KN

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