anonymous
  • anonymous
help me on this please.. The lower edge of a mural, 12 ft high, is 6ft above an observer’s eye. Under the assumption that the most favorable view is obtained when the angle subtended by the mural at the eye is maximum, at what distance from the wall should the observer stand?
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
welshfella
  • welshfella
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welshfella
  • welshfella
tan X = 18/x where x is distance of the eye from the wall tan Y = 6/x so tan X = 3 tan Y tan ( X - Y) has to be a maximum

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welshfella
  • welshfella
I can't think of an analytical way to do this but using the fact that tan X = 3 tan Y and a trial and error numerical method I get X = 60 and Y = 30 so the angle subtended by the mural = 30 degrees and the distance from the eye to the wall is easy to calculate tan 30 = 6 / x x = 6 / tan 30
welshfella
  • welshfella
this is at best an approximate answer
anonymous
  • anonymous
hello?
anonymous
  • anonymous
i dont understand how u get x=60 and y=30?
welshfella
  • welshfella
tan X = 3 tan Y i used trial and error i tried X = 55 so tan 55 = 3 tan Y this gave Y = 25.45 and X_Y = 29.54 X = 59 this gave X - Y= 29.1 X = 61 gave X - Y = 29.98 X = 60 gave X - Y= 30 so X - Y seems to peak at 30 degrees

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