If cos 0=3/5, use the pythagorean identities to find tan 0

Cos Ф = 3/5

As we know by the trigonometric ratios

Cos Ф = adjacent /hypotenuese

So it means

adjacent /hypotenuese = 3/5

Which means adjacent = 3 and hypotenuese = 5

Now using Pythagorean theorem we can find the opposite side

So opposite ^2 + 3^2 = 5^2

Opposite^2 + 9 = 25

subtract 9 from both sides

Opposite^2 = 16

Opposite = 4

Now tan Ф = opposite/adjacent = 4/3

So

tan Ф = 4/3