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  • AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A the portion C B subtends any angle \beta at P. If A P

AB is a vertical pole and C is its middle point. The end A is on the level ground and P is any point on the level ground other than A the portion C B subtends any angle \beta at P. If A P: A B=2: 1, then \beta=\ldots
 

Option: 1

\tan ^{-1}\left(\frac{4}{9}\right)


Option: 2

\tan ^{-1}\left(\frac{1}{9}\right)


Option: 3

\tan ^{-1}\left(\frac{5}{9}\right)


Option: 4

\tan ^{-1}\left(\frac{2}{9}\right)


Answers (1)

best_answer

\begin{aligned} & \tan (\alpha+\beta)=\frac{x}{2 x}=\frac{1}{2} \\ & \tan \alpha=\frac{x / 2}{2 x}=\frac{1}{4} \\ & \frac{1}{2}=\frac{\tan \alpha+\tan \beta}{1-\tan \alpha \cdot \tan \beta}=\frac{\frac{1}{4}+\tan \beta}{1-\frac{1}{4} \tan \beta} \\ & \frac{1}{2}-\frac{1}{8} \tan \beta=\frac{1}{4}+\tan \beta \\ & \frac{1}{4}=\frac{9}{8} \tan \beta \quad \therefore \quad \beta=\tan ^{-1}\left(\frac{2}{9}\right) \end{aligned}

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sudhir.kumar

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