Results 1 to 2 of 2

Math Help - tower question

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    27

    tower question

    China's leaning tower has a height of 47m. It makes an angle of 87.2 degrees with the ground. There is a specific point on the ground where you can be equidistant from both the top and bottom of the tower. How far is this point from the base of the tower?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,546
    Thanks
    539
    Hello, andrewpark2!

    China's leaning tower has a height of 47m and makes an angle of 87.2 with the ground.
    There is a point on the ground which is equidistant from the top and bottom of the tower.
    How far is this point from the base of the tower?
    Code:
                                   A
                                  o
                               *
                            * 87.2*
                     x   *
                      *             * 47
                   *
                *                    *
             *  5.6           87.2
        C o   *   *   *   *   *   *   o B
                        x

    The tower is: AB = 47
    \angle B = 87.2^o

    The special point is at C\!:\;\;x = CA =CB

    Since \Delta ABC is isosceles: . \angle A = 87.2^o,\;\angle C = 5.6^o


    Law of Cosines: . 47^2 \;=\;x^2+x^2-2(x)(x)\cos5.6^o

    . . . . . 47^2 \:=\:2x^2 - 2x^2\cos5.6^o \;=\;2x^2(1 - \cos5.6^o) \;=\;4x^2\left(\frac{1-\cos5.6^o}{2}\right)

    . . . . . 47^2 \;=\;4x^2\sin^2\!2.8^o \quad\Rightarrow\quad x^2 \:=\:\frac{47^2}{4\sin^2\!2.8^o} \quad\Rightarrow\quad x \:=\:\frac{47}{2\sin2.8^o}


    Therefore: . x \;=\;481.0667... \;\approx\;481\text{ m}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. square tower question
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: April 27th 2010, 02:54 AM
  2. Height of a Tower
    Posted in the Trigonometry Forum
    Replies: 15
    Last Post: February 28th 2010, 05:26 PM
  3. Tower of Hanoi Question
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: January 23rd 2010, 04:11 PM
  4. Tower Law problem
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 12th 2009, 04:30 PM
  5. Tower Question
    Posted in the Geometry Forum
    Replies: 4
    Last Post: June 21st 2008, 08:53 AM

Search Tags


/mathhelpforum @mathhelpforum