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Q. A particle is thrown over a triangle from one end of a horizontal base and after grazing the vertex falls on the other end of the base. If $30^\circ $ and $60^\circ $ be the base angles and $\theta $ the angle of projection then $tan\theta $ is

NTA AbhyasNTA Abhyas 2022

Solution:

Solution
$tan \theta =tan ⁡ \alpha +tan ⁡ \beta $
$tan \theta =tan ⁡ 30^{o}+tan ⁡ 60^{o}$
$tan \theta =\frac{1}{\sqrt{3}}+\sqrt{3}$
$tan \theta =\frac{4}{\sqrt{3}}$