The areas of the regions illustrated above can be found from the equations
(1)
|
(2)
|
Since we want to solve for three variables, we need a third equation. This can be taken as
(3)
|
where
(4)
|
(5)
|
leading to
(6)
|
Combining the equations (1), (2), and (6) gives the matrix equation
(7)
|
which can be inverted to yield
(8)
| |||
(9)
| |||
(10)
|