A camera is supplied with two interchangeable lenses, whose focal lengths are $46\mathrm{.}0$ and $130\mathrm{.}0$ mm $.$ A woman whose height is $1\mathrm{.}65$ m stands $8\mathrm{.}00$ m in front of the camera. What is the height $($including sign$)$ of her image on the image sensor$,$ as produced by $($a$)$ the $46\mathrm{.}0$ mm lens and $($b$)$ the $130\mathrm{.}0-$mm lens?

$($a$)$ Number $$ Units $$

$($b$)$ Number $$ Units $$