[Math] Calculate width and height to give to rectangle to achieve required size after rotation

Question

My goal is to create a rotated rectangle with a size to my specification. I begin with a regular rectangle which gets rotated 45 degrees.

Now I know I have succeeded to calculate the width and height after the rotation using;

rotatedSize = (sin(0.785398163) * originalSize) * 2;

So when I want a rotated rectangle of 100×100 my formula is;

100 = (sin(0.785398163) * originalSize) * 2;

Now I am not very good at math but I know there is a way to solve this formula, can anyone assist me in solving it?

Answer 1

You need $\sin \frac{\pi}{4}=\frac{\sqrt{2}}{2}\approx 0.707\ $, so originalsize$=\frac{100}{\sqrt{2}}\approx 70.71$