Figure $1$: The scene in the image is from the motion picture "A Star is Born" staring Lady Gaga and Bradley Cooper.

$[7$ points$]$ Given Figure $1,$ assume that $($i$)$ there is no radial distortion in the picture and $($ii$)$ the camera is level with the ground, such that the horizontal and vertical lines in the image are parallel.

$($a$)$ Draw the horizon of the ground plane.

$($b$)$ Find the height of the person in the picture as denoted by the line segment. In the scene, the real world height of the toilet stall is $180$ cm $.$ Use a ruler on a printed version of the page containing the figure to find the appropriate image lengths. Make sure to clearly label the points and lines used in the image. Show all your calculations. Your final answer should be approximated up to two decimal points.