Question

A particle is thrown at angle $\theta$ with horizontal over a triangle from one end of a horizontal base and grazing the vertex falls on the other end of the base. If $\alpha$ and $\beta$ be the base angles, find $\tan \alpha +\tan \beta$.

• A. $\tan \theta$
• B. $\cos \theta$
• C. $\sin \theta$
• D. $\cot \theta$

Answer 1

The correct option is A $\tan \theta$


From diagram, $\tan \alpha =\frac{h}{a},\tan \beta =\frac{h}{b}$
Also, we know the equation of trajectory as,
$y=x\tan \theta [1-\frac{x}{R}]$
$h=a\tan \theta [1-\frac{a}{a+b}]$
$h=\frac{ab}{(a+b)}\tan \theta$
$\tan \theta =h[\frac{1}{a}+\frac{1}{b}]$
$\tan \theta =\tan \alpha +\tan \beta$