Hi

I want to calculate theta1 and theta2 . anyone help me.

Printable View

- Feb 26th 2008, 09:21 PMkumarrectangle angles
Hi

I want to calculate theta1 and theta2 . anyone help me. - Feb 26th 2008, 09:54 PMearboth
- Feb 26th 2008, 10:03 PMkumar
Hi earboth

Thanks for ur reply. I have to take full lenght and width of rectangle , or length/2 or widht /2. Is this will give correct angle in degrees? if not what I have to do for getting angle in degrees. - Feb 27th 2008, 12:06 PMearboth
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 $\displaystyle \tan^{-1}$ :

$\displaystyle \theta_1 = \tan^{-1}\left(\frac lw\right)$ - Feb 27th 2008, 08:29 PMkumar
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) - Feb 27th 2008, 09:34 PMearboth
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. - Feb 27th 2008, 10:23 PMkumar
Thanks earboth.