A) \[50{}^\circ \]
B) \[80{}^\circ \]
C) \[40{}^\circ \]
D) \[100{}^\circ \]
Correct Answer: C
Solution :
tan (2\[\theta \] + \[45{}^\circ \]) = cot 3\[\theta \] = tan \[\left( 90{}^\circ -3\theta \right)\] \[\Rightarrow \]\[2\theta +45{}^\circ =90{}^\circ -3\theta \] \[\Rightarrow \]\[5\theta =90{}^\circ -45{}^\circ =45{}^\circ \] \[\therefore \]\[\theta =9{}^\circ \] AB = Length of the thred = 150 metre \[\angle \]BAC =\[60{}^\circ \] In \[\Delta \]ABC. sin \[60{}^\circ \] =\[\frac{BC}{AB}\Rightarrow \frac{\sqrt{3}}{2}=\frac{BC}{150}\] \[\Rightarrow \]BC \[=150\times \frac{\sqrt{3}}{2}=75\sqrt{3}\] metreYou need to login to perform this action.
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