I have the top left corner and bottom right corner coordinates of a rectangle.
The length of the diagonal is just the distance between the top left corner and bottom right corner.
How can i solve for the length of the sides of the rectangle.
[Math] How to calculate the length of the sides of a rectangle given the diagonal coordinates
geometry
Related Solutions
You need the Pythagorean theorem. The distance is $\sqrt{140^2+300^2} \approx 331$ The angle from the horizontal to the diagonal (note you need two lines to define an angle) is $\frac{180}{\pi}\arctan(\frac{140}{300})$ assuming your source of arctangents gives radians. If not, delete the $\frac{180}{\pi}$ multiplier (that is just the radian to degree conversion)
Let's start with a careful diagram with lots of labels to make it easier to discuss. I've also exaggerated the width $T$ of the bar to be sure we're talking about the same placement and to make it easier to label things. I also changed $x$ to $X$ and $a$ to $\alpha$. You are given $W$, $H$, and $T$, and want to determine $X$ and $\alpha$. Because of various parallel and perpendicular things, I've labeled some more angles $\alpha$.
Looking at $\triangle ABF$ and $\triangle EGA$, $\sin\alpha=\frac{W}{X}=\frac{T}{AE}$, so $AE=\frac{TX}{W}$. In $\triangle ABF$, applying the Pythagorean theorem, $$X^2=W^2+(H-AE)^2=W^2+\left(H-\frac{TX}{W}\right)^2.$$ Solving for $X$ in terms of $W$, $H$, and $T$ (with the assumption that $0< T< H< W$) gives $$X=\frac{-HWT+W^2\sqrt{H^2+W^2-T^2}}{W^2-T^2}.$$
Knowing $X$, since $\sin\alpha=\frac{W}{X}$, $\alpha=\arcsin\frac{W}{X}$.
Best Answer
There are infinitely many answers with the information given. As you can easily imagine, there are lots of rectangles, of different sizes that have the same diagonal. Certainly, if the sides of the rectangle are $a$ and $b$, and the length of the diagonal is $d$, then $a^2+b^2=d^2$. You're trying to use one number $d$ to find two numbers $a$ and $b$. This should upset you, philosophically. To solve the problem, we need more information. Either the other diagonal, or perhaps you seek only integer solutions...?