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

Answer 1

Answer: (B)

$\frac{2}{9}$

Answer 2

$\tan \theta=\frac{1}{4}$
$\tan \left(\theta+\beta\right)=\frac{1}{2}$
$\therefore \frac{\frac{1}{4}+\tan\beta}{1-\frac{1}{4}\tan\beta}=\frac{1}{2}$
Solving tan $\beta=\frac{2}{9}$