Do these equations represent the distance of a point from the origin on both axes?

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Triangle and the equations

Does these equations somehow represent the distance between the leftmost point (assumed as origin) and the point (x,y), with the distance on the x axis being the first equation and the distance on the y axis being the second equation? If so, how; and if not, what do they represent?

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That is a strange picture.

The formulas give the new coordinates of the point you get when you rotate the point $(x,y)$ through angle $\theta$. about the origin.

Try some examples to confirm that.