They would be similar triangles because they cannot be congruent due to the fact that the side lengths are different. They are dilutions of each other which again proves that they are similar, not congruent.
Sin (tan^(-1)X)
Sin (1/tan X)
Sin (1/1 / tan X/1)
Tan X = sin X/cos X
Sin (1/1 / sin X/cos X)
Sin (1/1 • cos X/Sin X)
Sin (cos X/sin X )
Cos X.
I believe the correct answer is cos X.
Explanation
Let's first graph the elements:
Using the distance formula we get:

In order to find what one part is in a ratio, you have to add the ratio up ( 5+ 3) and divide it by the number you're looking for (56). In this case, you get 56/8, which gives you 7. Therefore, each part is worth 7. You then have to multiply both sides of the ratio (5 and 3) by 7. 5x7= 35. 3x7= 21.
Therefore, 56 divided into the ratio of 5:3 is 35:21