Ricky Bobby Views Mona Lisa at Louvre

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SUMMARY

The discussion centers on calculating the optimal distance for Ricky Bobby to stand from the Mona Lisa at the Louvre to maximize the vertical angle subtended by the painting. The painting's dimensions are 77 cm by 53 cm, positioned 236 cm above the floor, while Ricky's eye level is 161 cm. The mathematical approach involves using trigonometric functions, specifically tangent, to derive the angles and subsequently determine the distance from the wall. The critical points and derivatives are calculated to find the optimal standing position.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent.
  • Familiarity with calculus concepts such as derivatives and critical points.
  • Knowledge of geometry related to angles and distances.
  • Ability to convert angles from radians to degrees.
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  • Explore the relationship between angles and distances in geometry.
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Students studying calculus, geometry enthusiasts, and anyone interested in applying mathematical concepts to real-life scenarios, particularly in art and architecture contexts.

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Homework Statement


Ricky Bobby, the calculusmeister, arrives early at the Louvre in Paris for the Da Vinci Code showing of "Mona Lisa". He has a choice of where to stand to view the portrait. He wants to be in position so that picture subtends the largest possible vertical angle at his eye. The dimension of the painting is 77 x 53 cm. It is positioned on its own wall in the Louvre so that the bottom of the picture is 236 cm above the floor. How far back from the wall should Ricky stand? Ricky Bobby's eye is 161 cm above the floor.


Homework Equations


Im not sure if I am on the right track and i have to turn it into degrees how do i do that?


The Attempt at a Solution


tanX=75/x
tanB=152/x

B-X=theta tanB-tanX/1+(tanB)(tanX) (1) (152/x-75/x)x^2/(1+(152/x)(75/x)(x^2) (2) 77x/x^2+11400

(3) f'(x)=(x^2+11400)(77)-(77x)(2x)/(x^2+11400)^2

-77x^2+(11400 x 77)/(x^2+11400) critical # + or - 106.770778
tanX= 75/.7024393753
tanB= 152/1.423610467

B-X= .7211710917
 
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Since you haven't said what C and B represent in this problem, there is no way of determining whether what you have done is correct.