Calculate the value of \(Y _ { \mathrm { Q } }\) and show that \(Y _ { \mathrm { R } } = 120\).
The inn sign is hung from a framework, ABCD , by means of two light vertical inextensible wires attached to the sign at Q and R and the framework at B and C , as shown in Fig. 3.2. QR and BC are horizontal. The framework is made from light rigid rods \(\mathrm { AB } , \mathrm { BC } , \mathrm { CA }\) and CD freely pin-jointed together at \(\mathrm { A } , \mathrm { B }\) and C and to a vertical wall at A and D . Fig. 3.3 shows the dimensions of the framework in metres as well as the external forces \(X _ { \mathrm { A } } \mathrm { N } , Y _ { \mathrm { A } } \mathrm { N }\) acting at A and \(X _ { \mathrm { D } } \mathrm { N } , Y _ { \mathrm { D } } \mathrm { N }\) acting at D .
You are given that \(\sin \alpha = \frac { 5 } { 13 } , \cos \alpha = \frac { 12 } { 13 } , \sin \beta = \frac { 4 } { 5 }\) and \(\cos \beta = \frac { 3 } { 5 }\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8fb49c8b-92e5-49e5-9a3a-e8391c82d9a1-4_543_526_1420_253}
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\caption{Fig. 3.2}
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\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{8fb49c8b-92e5-49e5-9a3a-e8391c82d9a1-4_629_793_1343_964}
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\caption{Fig. 3.3}
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