How to find one side of a rectangle, if I have other side and slope

Question

So suppose I have the width of a rectangle that is 1000 cms and its slope that is at 20 degrees. How can I calculate the other length required for the height of this rectangle....

Answer 1

Hint:

Suppose $x$ is the basis of the rectangle and $\alpha$ the slope of the diagonal ( in your case $\alpha=20°$), than the height is $h= x \tan \alpha$ and the area is

$ A= x \times h =x \times x \tan \alpha $

Here the solution:

$x^2=\dfrac{A}{\tan \alpha}=\dfrac{1000}{\tan (20°)}=2747 \Rightarrow x=\sqrt{2747}=52.42$