Given
[tex]\sin\theta=\frac{2}{3}[/tex]
Find
which of the following are possible?
Explanation
as we know ,
[tex]\begin{gathered} \sin\theta=\frac{P}{H} \\ \end{gathered}[/tex]
so , H = 3 , P = 2
then
[tex]\begin{gathered} B=\sqrt{H^2-P^2} \\ B=\sqrt{9-4} \\ B=\sqrt{5} \end{gathered}[/tex]
so ,
[tex]\begin{gathered} \cos\theta=\frac{B}{H}=\frac{\sqrt{5}}{3} \\ \\ \tan\theta=\frac{P}{B}=\frac{2}{\sqrt{5}} \\ \\ sec\theta=\frac{1}{\cos\theta}=\frac{3}{\sqrt{5}} \end{gathered}[/tex]
Final Answer
Hence , the correct options are B and C
