How Do Strangely Aligned Capacitor Plates Affect Distance Calculations?

[mateomy]

Working along step-by-step with a text and I'm stumped as to how they reached a conclusion. In the first picture you see two plates aligned at an unspecified angle, theta. One plate is at a potential V and the other is grounded. The distance between the plates at one end is d, and at the other end d+a. You can see in the second picture how they've set it up with respect to a two dimensional coordinate system. Maybe it's late and I'm braindead or maybe not in any even I can't see how they've formed the relationship between b,d and a to determine the distance between the actual origin and the intersection of the plates (dotted lines in picture three). Can anybody enlighten me?

Thanks.

 

[mateomy]

P.S. the whole point is to find the potential, but this is where I'm hung up.

 

[robphy]

In the triangle (in x<0) with base OO' and the height d, you have
tan(theta_0)=d/(OO').

In the trapezoid (in x>0), draw the horizontal at height d to form a similar triangle,
with base b and height a. Thus
tan(theta_0)=a/b.

 

[mateomy]

Truly geometry is my weakest link. Thank you.