Results 1 to 4 of 4

Math Help - estimating error please help

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    2

    estimating error please help

    A surveyor,standing 30ft from the base of a building,measures the angle of elevation to the top of the building to be 75 degree.How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by turkeyy View Post
    A surveyor,standing 30ft from the base of a building,measures the angle of elevation to the top of the building to be 75 degree.How accurately must the angle be measured for the percentage error in estimating the height of the building to be less than 4%?
    Well the height is:

    h=30 \tan(\theta)

    where theta is the angle of elevation of the top of the building. Now suppose that we measure the elevation with error \Delta \theta, and then compute a height h+\Delta h where \Delta h is the error in the height. so:

    h+\Delta h = 30 \tan(\theta + \Delta \theta)\approx 30 \tan(\theta)+\Delta \theta \frac{d}{d \theta}[30 \tan(\theta)]  <br />
=h+\Delta \theta \frac{d}{d \theta}[30 \tan(\theta)]<br />

    Can you take it from there?

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,683
    Thanks
    615
    Hello, turkeyy!

    A different interpretation . . . a different approach.


    A surveyor, standing 30ft from the base of a building,
    measures the angle of elevation to the top of the building to be 75.
    How accurately must the angle be measured for the percentage error
    in estimating the height of the building to be less than 4%?
    The wording is somewhat vague.
    I will assume that 75 is the exact angle of elevation.

    Let H = the exact height of the building.

    We have: . \tan75^o \:=\:\frac{H}{30} \quad\Rightarrow\quad H \:=\:30\tan75^o .[1]


    Suppose he measures an angle of elevation of \theta degrees.

    Then his estimated height h is: . h \:=\:30\tan\theta .[2]


    Divide [2] by [1]: . \frac{h}{H} \:=\:\frac{30\tan\theta}{30\tan75^o} \quad\Rightarrow\quad \frac{h}{H} \:=\:\frac{\tan\theta}{\tan75^o}

    \frac{h}{H} is the ratio of the estimated height to the exact height.
    . . We want this to be between 96% and 104%.

    . . \begin{array}{ccccc}<br />
0.96 & < & \dfrac{\tan\theta}{\tan75^o} & < & 1.04 \\ \\[-3mm]<br />
3.582768775 & < & \tan\theta & < & 3.88133284 \\ \\[-3mm]<br />
74.40^o & < & \theta & < & 75.55^o\end{array}


    Therefore, the angle must be measured to 0.5.

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by Soroban View Post
    Hello, turkeyy!

    A different interpretation . . . a different approach.

    The wording is somewhat vague.
    I will assume that 75 is the exact angle of elevation.
    It does not matter if the 75 degrees is exact or approximate, to the accuracy involved in the calculation they give the same result.

    Also the required accuracy form your calculation must be ~= +/- 0.6 degrees.

    CB
    Last edited by CaptainBlack; November 8th 2008 at 07:08 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. estimating error Taylor polynomials
    Posted in the Calculus Forum
    Replies: 4
    Last Post: July 26th 2011, 08:44 AM
  2. Replies: 0
    Last Post: August 11th 2010, 01:02 AM
  3. estimating remainder and error
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 16th 2010, 05:53 PM
  4. Margin of Error and Estimating Population Mean
    Posted in the Statistics Forum
    Replies: 1
    Last Post: May 1st 2009, 07:15 AM
  5. Estimating error using differentials
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 20th 2007, 08:08 PM

Search Tags


/mathhelpforum @mathhelpforum