Cannot understand how arctan for angle theta is calculated

[Guest]

Please see the attachment.

I'm struggling to understand why the ratios as shown are the arctan of angle theta.

[nathi123]

[tex]\beta = \delta +\tita[/tex] (external angle for triangle with angles [tex]\delta and \tita )[/tex]
[tex]tg\beta = \frac{d_{1 }}{d} ; tg\delta = \frac{d_{1 }}{d_{2}+L}[/tex] (defined for tangent to angle in a rectangular triangle)
[tex]tg \tita =tg(\beta - \delta ) = \frac{tg\beta-tg\delta}{1+tg\beta.tg\delta} = \frac{d_{1 }L}{d_{2 }^{2}+Ld_{1 }+d_{1 }^{2}}[/tex].

[Guest]

proof.png (49.81 KiB) Viewed 1629 times

Thanks, this really helped me out.

You had a small typo in the denominator (should be d2^1 + d2L + d1^1) as shown in the attachment.