A) \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
B) \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
C) \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]
D) \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
Correct Answer: D
Solution :
\[1\times \sin 90=\frac{2}{\sqrt{3}}\sin (90-\alpha )\] \[\Rightarrow \]\[\cos \alpha =\frac{\sqrt{3}}{2}\] So \[sin\alpha =\sqrt{1-\frac{3}{4}}=\frac{1}{2}\] Now, \[1\times \sin \theta =\frac{2}{\sqrt{3}}\sin \alpha \] \[=\frac{2}{\sqrt{3}}\times \frac{1}{2}=\frac{1}{\sqrt{3}}\] \[\Rightarrow \]\[\theta ={{\sin }^{-1}}\frac{1}{\sqrt{3}}\]You need to login to perform this action.
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