Given an elliptical ranch with dimensions $2*$R units horizontally and $1$ unit vertically, a goat is tied to the fence inside the ranch using a leash of length r units. The angle formed between the point of tying and the horizontal axis is $\backslash$theta $.$

To determine the area of grass the goat can graze, the following inputs are provided as shown in the image below:

R half of the horizontal dimension of the ranch,

r the length of the leash, and

$\backslash$theta the angle formed by the point of tying and the horizontal axis.

Write a program that takes these three inputs as floating$-$point numbers on separate lines and prints the total area of grass the goat can graze, rounded to three decimal points. The code is not passing testcases. I will attach a c$++$ code which passes $5$ test cases. Please debug it to pass all the $10$ test cases #include

#include

#include

double grazing$\_$area$($double R$,$ double r$,$ double theta$)\{$

double theta$\_$rad $=$ M$\_$PI $*$ theta $/142\mathrm{.}0$;

double b $=1\mathrm{.}0/2\mathrm{.}0$;

double sector$\_$area $=0\mathrm{.}5*$ r $*$ r $*$ theta$\_$rad;

double triangle$\_$area $=0\mathrm{.}5*$ r $*($R $-$ r $*$ cos$($theta$\_$rad$))$;

double grazing$\_$area $=$ sector$\_$area $-$ triangle$\_$area;

if $($grazing$\_$area $>$ M$\_$PI $*$ R $*$ b$)\{$

grazing$\_$area $=$ M$\_$PI $*$ R $*$ b;

$\}$

return round$($grazing$\_$area $*1000\mathrm{.}0)/1000\mathrm{.}0$;

$\}$

int main$()\{$

double R$,$ r$,$ theta;

std::cin $>>$ R $>>$ r $>>$ theta;

double area $=$ grazing$\_$area$($R$,$ r$,$ theta$)$;

std::cout $<<$ area $<<$ std::endl;

return $0$;

$\}$