# Math Help - rectangle angles

1. ## rectangle angles

Hi

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

2. Originally Posted by kumar
Hi

I want to calculate theta1 and theta2 . anyone help me.
The rectangle's width is w and the rectangle's length is l.

Then

$\tan(\theta_1) = \frac lw$ ............ and

$\tan(\theta_2) = \frac wl$

3. 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.

4. Originally Posted by kumar
Hi earboth

Thanks for ur reply. I have to take full lenght and width of rectangle , or length/2 or widht /2.
That doesn't matter because all rectangles in your drawings are similar and therefore the ratio is constant.

Originally Posted by kumar
Is this will give correct angle in degrees? if not what I have to do for getting angle in degrees.
You have to use a calculator. Set it to degree mode.

Then $\theta_1 = \arctan\left(\frac lw\right)$ or probably the key of your calculator is labeled $\tan^{-1}$ :

$\theta_1 = \tan^{-1}\left(\frac lw\right)$

5. 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)

6. Originally Posted by kumar
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

$\tan(\theta) = \underbrace{\frac{\frac w2}{\frac l2}}_{\text{small rectangle}} = \frac{2w}{2l} = \underbrace{\frac wl}_{\text{whole rectangle}}$

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.)

$\theta_1 = \theta_4 = \theta_5 = \theta_8$ and $\theta_2 = \theta_3 = \theta_6 = \theta_7$

2.)

$\theta_1 + \theta_2 = \theta_3 + \theta_4 = \theta_5 + \theta_6 = \theta_7 + \theta_8 = 90^\circ$

But I can't help you with the exact value of the angle $\theta_i$ because I don't know the measures of the rectangle.

7. Thanks earboth.