javascript - How can I calculate the size of an outer rectangle when it is rotated and must encompass an inner rectangle totally -

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I have many answered questions, explaining how to calculate the bounding box of the curved rectangle But what i need to do is reverse

Red Rectangle A is described as: 

  var box = {x: 0, y: 0, w: 100, h : 200};

And the dimension of blue rectangle b is exactly , when it is rotated not .

Given that the rectangle B has been rotated around its center point and given in the angle of radians, I use the minimum size Rectangle <<> B may occur when rectangular A should always fit inside it while maintaining its original aspect ratio (as previously mentioned, rectangular A similar)

Enter image details here

If you label edges of rectangles and attract an extra line (green in the diagram), you can see what you need to calculate:

Enter image details here

then c = a * Cos (θ) + b * sin (Θ)

and d = b * c / a


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