Question

Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP=2AB$. If $\angle BPC=\beta$ , then $\tan \beta$ is equal to:

• A. $\frac{6}{7}$
• B. $\frac{1}{4}$
• C. $\frac{2}{9}$
• D. $\frac{4}{9}$

Answer 1

The correct option is C $\frac{2}{9}$

According to the question, the figure will be:

$\tan (\theta +\beta )=\frac{1}{2}\text{and}\tan \theta =\frac{1}{4}\Rightarrow \tan (\theta +\beta )=\frac{\frac{1}{4}+\tan \beta }{1-\frac{1}{4}\tan \beta }=\frac{1}{2}\Rightarrow \tan \beta =\frac{2}{9}$