Hi
I want to calculate theta1 and theta2 . anyone help me.
That doesn't matter because all rectangles in your drawings are similar and therefore the ratio is constant.
You have to use a calculator. Set it to degree mode.
Then $\displaystyle \theta_1 = \arctan\left(\frac lw\right)$ or probably the key of your calculator is labeled $\displaystyle \tan^{-1}$ :
$\displaystyle \theta_1 = \tan^{-1}\left(\frac lw\right)$
Hello earboth
Thanks. That is one rectangle only, for explanation only I created diagonals, and mid lines( vertical, horizondal). I cannot use calculator(this is for my project , programatically i need), I need a formula to get angle in degrees. please explain to get all angles of diagonals from the mid point.( theta1 to theta8)
If you calculate
$\displaystyle \tan(\theta) = \underbrace{\frac{\frac w2}{\frac l2}}_{\text{small rectangle}} = \frac{2w}{2l} = \underbrace{\frac wl}_{\text{whole rectangle}}$
it doesn't matter which rectangle you use because all marked rectangles are similar to the complete rectangle. (see attachment)
By law of symmetry you can proof that
1.)
$\displaystyle \theta_1 = \theta_4 = \theta_5 = \theta_8$ and $\displaystyle \theta_2 = \theta_3 = \theta_6 = \theta_7$
2.)
$\displaystyle \theta_1 + \theta_2 = \theta_3 + \theta_4 = \theta_5 + \theta_6 = \theta_7 + \theta_8 = 90^\circ$
But I can't help you with the exact value of the angle $\displaystyle \theta_i$ because I don't know the measures of the rectangle.