1.
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\caption{Figure 1}
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A particle of weight \(W\) newtons is attached at \(C\) to two light inextensible strings \(A C\) and \(B C\). The other ends of the strings are attached to fixed points \(A\) and \(B\) on a horizontal ceiling. The particle hangs in equilibrium with \(A C\) and \(B C\) inclined to the horizontal at \(30 ^ { \circ }\) and \(50 ^ { \circ }\) respectively, as shown in Figure 1.
Given that the tension in \(B C\) is 6 N , find
- the tension in \(A C\),
- the value of \(W\).