need equations for a rectangle in a rectangle

[chibois]

these are 2 rectangles (90 degree angles)
x<3y<9x

i'm trying to write a program where u input an image, it rotates a logo and expands it to cover the image, i need an equation for the degrees "r" and the height "a" given x and y as inputs. its been 6 years since i've taken geometry and trig and i'm quite stumped as to how to make the equations.

thanks in advance!

 

[Denis]

The smaller and larger right triangles are similar, which "sweetens the deal"!
Without going into details (hate typing):

u = (3x - y) / 8
v = (3y - x) / 8

a = SQRT(u^2 + v^2) : in other words, a is length of the hypotenuse of right triangle with legs = u and v

r = ASIN(u / a)

Try it; let x=39 and y=53
You'll get u=8, v=15, a=17 and r = ~28.072 degrees
The larger right triangle becomes: 24-45-51 (what does that tell you?)