Question

the mona lisa hangs about 6 ft above the ground the dimensions are 21 by 30 in^2 = (w x h). How close to the painting should someone who is 5'7'' stand in order to get the best view of the painting? Assume the direct line of sight to the wall where La Jaconde hangs is 5'4'' (why?).

Answer 1

e is the angle subtended by the eye of the person for the view of the painting. For the best view of the painting this angle should be maximum. Consider the following. hd tan (0a) Differentiate both sides with respect to x h+d de da sec (0+a) dx 2. dx Therefore, de da hd s2(0+a) + CO dx dx h d (h- (x+(p+u)) hd (2x(p+)) tan a is given as follows: h tan a =- Therefore,

d da h -1 tan dx dx h h Therefore, de is given as follows: dx de hd da (h+d)+x* 2. dx h d h (h+d)+x h x de should be zero. dx For 0 to be maximum Therefore de 0 dx h+d h 0 _ (+d)' 2 Il

Rearrange for x. h hd (t+ (p+4) h'hx dhd = h + 2hd +hd2 h h+x 2 hd+ha d x Vh(h+d) Therefore, the optimum distance is given as follows

h- at Н Since, the direct line of sight is at 5 feet 4 inches from the ground and painting hangs 6 feet from the ground h is given as follows h (65'4") =8 The height of the painting is given as follows: d 30 Therefore, the optimum distance to look at the painting is given as follows: (р+ч)ч: (8")(30"+8") 17.43