**Department of Mathematics
Education**

**J. Wilson, EMAT 6680**

** **

A 4 by 4 picture hangs on a wall such that its bottom edge is 2 ft above your eye level. How far back from the picture should you stand, directly in front of the picture, in order to view the picture under the maximum angle? Side view:

First observe that angles *θ* and v
are the arctangent values of the ratios a”/b and a’/b respectively.

Consequently

.

Determining the zeros for the
first order derivative of r with respect to *b* and disregarding the negative root (it’s behind the wall)

.

shows that r has its sole positive maximum at feet from the wall.