$\%$ Define the coordinates of the apple

x $=<3>$;

y $=<5>$;

$\%$ Define the lengths of the robot arm

a $=<10>$;

b $=<15>$;

$\%$ Calculate the distance from the robot to the apple

r $=$ sqrt$($x$^2+$ y$^2)$;

$\%$ Calculate theta$1$ using the four$-$quadrant inverse tangent

theta$1=$ atan$2($y$,$ x$)$;

$\%$ Calculate theta$2$ using the law of cosines

theta$2=$ acos$(($r$^2+$ a$^2-$ b$^2)/(2*$ a $*$ r$))$;

$\%$ Display the results

disp$([\text{'}$Theta$1$: $\text{'},$ num$2$str$($theta$1)])$;

disp$([\text{'}$Theta$2$: $\text{'},$ num$2$str$($theta$2)])$;