Question

A person walking along a canal observes that two objects are in the same line which is inclined at an angle $\alpha$ to the canal. He walks a distance $C$ for the and observes that the objects subtended their greatest angle $\beta$ then the distance between the object is

• A. $\frac{2C\sin \alpha \sin \beta }{\cos \beta -\cos \alpha }$
• B. $\frac{2C\sin \alpha \sin \beta }{\cos \alpha -\cos \beta }$
• C. $\frac{2C\sin \alpha \sin \beta }{\cos \alpha +\cos \beta }$
• D. $\frac{2C\cos \alpha \cos \beta }{\sin \alpha -\sin \beta }$

Answer 1

Answer: (C)

$\frac{2C\sin \alpha \sin \beta }{\cos \alpha +\cos \beta }$

$\tan \alpha =\frac{h_1}{a}-\left(1\right),\tan \alpha =\frac{h_2}{a+b}-\left(2\right),\tan \beta =\frac{h_1}{a-c}-\left(3\right)$
$\tan \beta =\frac{h_2}{a+b-c}-\left(4\right)$
$\tan \beta (a+b-c)=\tan \alpha (a+b)$ (From (1) & (3))
$\tan \alpha a=\tan \beta (a-c)$ (From (2) and (4))
$a=\frac{\tan \beta c}{\tan \beta -\tan \alpha }$