Results 1 to 2 of 2

Math Help - Optimization problem

  1. #1
    HMV
    HMV is offline
    Newbie
    Joined
    Oct 2008
    Posts
    20

    Optimization problem

    A photographer is taking a picture of a four-foot painting hung on the art gallery. The camera lens is 1 foot below the lower edge of the painting. How far should the camera be from the painting to maximize the angle subtended by the camera lens?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    Let x be the distance the camera is from the painting.

    Then, we have two triangles.

    Angle {\theta} is the one we need.

    So, we have tan^{-1}(\frac{5}{x})-tan^{-1}(\frac{1}{x})

    Differentiate, set to 0 and solve for x.

    We could also use cot:

    cot^{-1}(\frac{x}{5})-cot^{-1}(x)
    Attached Thumbnails Attached Thumbnails Optimization problem-camera.gif  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] optimization problem
    Posted in the Calculus Forum
    Replies: 12
    Last Post: October 6th 2011, 03:47 PM
  2. Optimization problem
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: March 4th 2011, 10:58 PM
  3. Optimization Problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2009, 07:41 PM
  4. help!!!- optimization problem
    Posted in the Calculus Forum
    Replies: 2
    Last Post: December 13th 2008, 04:59 PM
  5. Optimization Problem
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: April 8th 2008, 05:55 PM

Search Tags


/mathhelpforum @mathhelpforum