$(30$ pts$)$ Consider the object in the figure below that is an equilateral triangle centered at

the origin, each side of which is of length a and one side of which is parallel to the $x$ axis.

Suppose the object has constant linear attenuation coefficient $$ and is being imaged in a $1G$

CT scanner.

Figure $1$: Object geometry for the Question $5$

$($a$)(15pts)$ Find the formula for projection $g(l,60)$

$($b$)(5pts)$ Please sketch the figure of the above $g(l,60).$

$($c$)(10$ pts$)$ Let $b_{}(x,y)$ be the backprojection image. Write down the relationship between

$b$ and $g.$