Getting the Best View

Calculus Level 4

A 6 foot tall painting is placed on the wall so that the very bottom of the painting sits 7 feet above the floor. Suppose your eyes are 5 feet above the floor and that you are standing 6 feet from the painting. Let T be your line of sight with the top of the painting and B be your line of sight with the bottom of the painting. What is the absolute value of the rate the angle formed by T and B is changing (in radians per second) as you approach the painting at 3 feet per second?

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