To find tg α $tangentof\alpha$, we use the formula:

tg α = sin α / cos α

Given that cos α = 8/17, we first need to find sin α before we can find tg α.

Since sin^2 α + cos^2 α = 1, we can find sin α:

sin^2 α + $8/17$^2 = 1
sin^2 α + 64/289 = 1
sin^2 α = 1 - 64/289
sin^2 α = 225/289
sin α = √$225/289$ sin α = 15/17

Now that we have sin α, we can find tg α:

tg α = sin α / cos α
tg α = $15/17$ / $8/17$ tg α = 15/8

Therefore, tg α = 15/8.