Answer
$\dfrac{17}{6}$
Work Step by Step
Since, the interior angles of a triangle add up to $180^{\circ}$
Thus, we have $u=90-\alpha; v=90-\beta, \gamma =180-u-v$
So, $\gamma=180-(90-\alpha)-(90-\beta)=\alpha+\beta$
From the graph , we have $\tan \alpha =\dfrac{2}{3}$ and $\tan \beta =\dfrac{3}{4}$
Thus, $\tan (\alpha+\beta)=\dfrac{\tan \alpha+\tan \beta}{1-\tan \alpha \tan \beta}\\=\dfrac{\dfrac{2}{3}+\dfrac{3}{4}}{1-\dfrac{2}{3}\cdot \dfrac{3}{4}}\\=\dfrac{17}{6}$
