Q $8-01$: Use the Newton Raphson method to determine the length of the shortest ladder that reaches from the ground over the fence to touch the building's wall as shown in the following figure. Test it for the case where $h=d=4m.($Note: the blue vertical line is the fence$).$

$($a$)$ What is the engineering problem? $(3)$

$($b$)$ What is the mathematical problem? $(4)$

$($c$)$ Describe a numerical method to solve this problem. $(5)$

$($d$)$ Write and run Octave code to find the answer. $(15)$

$($e$)$ Develop a flowchart that exactly matches your code. $(5)$

$($f$)$ Write your engineering answer for a client. $(3)$