I'll TRY to answer this question as best as I can. (No? Bad pun? Ignore it.)
Anyways...
From angle R, we have a sine (opposite/hypotenuse) value of 3/5.
This means that we have a 3/4/5 right triangle.
Now, shifting to angle T (we'll have to visualize all of this), the "opposite" value of 3 from angle R becomes the "adjacent" value of angle T.
So, cosine of angle T is going to be 3/5.
Since we know that the adjacent value of T is 3, and that the hypotenuse is 5, the opposite side from T must be 4.
Tangent is opposite/adjacent, so tangent of angle T is 4/3.
