What is \tan \alpha+\tan \beta equal to?

Explanation

Using the side a = \frac{32}{\sqrt{17}}, we can determine the segments BF = \frac{8}{\sqrt{17}} and DE = \frac{26}{\sqrt{17}}. Thus, \tan \alpha = \frac{BF}{BC} = \frac{8}{32} = \frac{1}{4} and \tan \beta = \frac{DE}{DC} = \frac{26}{32} = \frac{13}{16}. Their sum is \frac{1}{4} + \frac{13}{16} = \frac{17}{16}.

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