Calculating the dimensions of a rectangle inside another rectangle I've been working on a geometrical issue for some time, but I cannot find an answer. I have a rectangle inside another rectangle. The only two values I know is the rotation of the smaller rectangle regarding the bigger rectangle α and also the diameter of the bigger rectangle d. 

Is there any way to calculate the dimensions of the inner rectangle or do I need more information?
 A: This is not enough information.
Imagine sliding the bottom point
to the right.
The side of the inner rectangle
to the right will get smaller
and the side to the left
will get larger.
However,
knowing the diameter
of the inner rectangle
is enough.
Suppose the sides
(width, height)
of the big rectangle
are $r$ and $s$,
and the sides
(width, height)
 of the
inner rectangle are
$u$ and $v$.
For the triangle 
on the lower right,
the legs are
$u \cos a$ and $u \sin a$.
For the triangle 
on the lower left,
the legs are
$v \cos a$ and $v \sin a$.
On the bottom,
we get
$u \cos a+v \sin a
=r$.
Similarly,
on the upper right,
the remaining part of
the height is
$v \cos a$,
so
$u \sin a+v \cos a = s$.
Squaring these,
$r^2
=(u \cos a+v \sin a)^2
=u^2\cos^2a + 2uv\cos a\sin a + v^2 \sin^2 a
$
and
$s^2 
(u \sin a+v \cos a )^2
=u^2\sin^2a+2uv\sin a \cos a + v^2\cos^2 a
$.
Adding these,
$d^2
= r^2+s^2
=u^2+v^2+4uv\sin a \cos a
=u^2+v^2+2uv\sin 2a
$.
From the top,
we have
$r
=v \sin a + u \cos a
$
and from the left
we have
$s 
=u \sin a + v \cos a
$.
However,
these are the same as before,
so we can not deduce anything further.
However,
if we know the diameter
of the inner rectangle,
say
$c^2 = u^2+v^2$,
then we have
$d^2
=c^2+2uv\sin 2a
$
so we can get
$uv$.
Knowing
$uv$ and
$u^2+v^2$,
we can get
$u+v$ and
$u-v$
($(u+v)^2 = u^2+v^2+2uv$
and
$(u-v)^2 = u^2+v^2-2uv$)
and thus get $u$ and $v$.
