how do i find the tangent of an unknown angle, when all the sides are given?

For a right triangle.

The tangent of an angle = opposite side length/adjaecent side length. (sin(x)/cos(x)) or (y/x) etc.

 - also note that sin(A) = a/c and cos(A) = b/c, and tan(A) = sin(A) / cos(A) = (a/c) / (b/c) which = (a/b)

In the case of angle A˚ tan(A) = a/b

In the case of angle B˚ tan(B) = b/a

In the case of angle C˚(or any right angle), tan(90˚) = undefined