help

Hint:

Use variables X and Y for the side lengths of the given rectangle.

All radii are congruent. One of the diagonal of the rectangle is a radii

So

x+4 = y + 2

x² + y² = x + 4  (Pythagorean theorem to find the diagonal)

Note that one side of the rectangle = r -2

And the other side  = r - 4

Using the Pythagorean Theorem  we have that

(r - 2)^2 + ( r - 4)^2 = r^2     simplify

r^2 - 4r + 4 + r^2 - 8r +16  = r^2

2r^2  -12r + 20  = r^2

r^2 - 12r + 20    = 0     factor

(r - 10) ( r - 2)  = 0

Setting each factor to  0  and solving for r we get that   r =  2  (reject)   or  r =  10 (accept)

I was looking for the angle whose cosine value is for 2 units larger then the value of sine.

And these numbers popped up:    0.8 and 0.6        sin(36.87°) = 0.6     cos(36.87°) = 0.8

I multiplied these numbers by 10,  and got the sides of a rectangle: a = 6   and  b = 8

Diagonal   d = r                      r² = a²+ b²           r = 10