C
The construction described creates the incenter of the circle and this point is equidistant from all vertices of a triangle.
Answer:
Length of the roof line is
. And depth of the shed is 
Step-by-step explanation:
Given front wall is 11.5 feet tall, back wall is 20.2 feet. And roof rises at 30° angle from the front wall.
Let
be the length of the roof line. And
the depth of the shed.
We can see it is a right angle triangle with opposite
(see the attachment)
Now,

Also,

So, Length of the roof line is
. And depth of the shed is 
The sum of angles in a triangle is 180°
So:
(x+7) + (11x-9) +32 = 180
15x +30 = 180
15x = 180-30
15x = 150
x = 150/15
x = 10°