Precalculus Question Pls help

cos = adj/hyp    which means AB = 6       sin c = opp/hyp =  6/10   

Tan = opp/adj   =  sin/cos      we either need AC    or   cos c   

we can find AC   via pythagorean theorem

6^2  + AC^2 = 10^2

AC^2 = 64

AC = 8                     so cos c = adj/hyp = 8/10

Tan c = sin c /cos c = 6/10  /  8/10  =  6/8

Using the definition:

$\cos B = \dfrac6{10} = \dfrac{AB}{BC}$

From this, we can conclude AB = 6.

By Pythagorean theorem, AC = 8.

$\tan C = \dfrac{AB}{AC} = \dfrac68 = \boxed{\dfrac34}$