Results 1 to 8 of 8

Math Help - find with with angles

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    61

    find with with angles

    Find the total grazing area of a goat. The animal is tied to the notheast corner of a 40' by 40' barn, by an 80' rope. The south side of the barn is extended by a fence. Assume that there is grass everywhere except inside the barn.
    ^^ This totally stumped on.

    A 16.0-inch chord is drawn in a circle whose radius is 10.0 inches. What is the angular size of the minor arc of this chord? what is the length of the arc, to the nearest tenth of an inch
    No idea how to find this!!

    PLEASE HELP!! This is urgent!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by pyrosilver View Post
    ^^ This totally stumped on.



    No idea how to find this!!

    PLEASE HELP!! This is urgent!
    did you draw the diagrams for the problems?

    note that in the first problem, you are finding the area for the sector of a circle.


    in the second problem, use the formula:

    c = 2r \sin \frac {\theta}2

    where r is the radius, c is the length of the chord, and \theta is the angle subtended by the chord
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2008
    Posts
    61
    Quote Originally Posted by Jhevon View Post
    did you draw the diagrams for the problems?

    note that in the first problem, you are finding the area for the sector of a circle.


    in the second problem, use the formula:

    c = 2r \sin \frac {\theta}2

    where r is the radius, c is the length of the chord, and \theta is the angle subtended by the chord
    I don't even have the slighest inkling on how to do it, I have no idea what you just said. Thanks for trying to help me, but do you think you could go into a little more depth/explanation?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by pyrosilver View Post
    I don't even have the slighest inkling on how to do it, I have no idea what you just said. Thanks for trying to help me, but do you think you could go into a little more depth/explanation?
    the first problem you won't understand until you draw the diagram. did you do that?

    the second problem is plug-and-chug. i gave you the formula. there is nothing for you to do but plug in numbers and evaluate


    the "angle subtended by the chord" is the minor angle they are talking about

    i left out the formula for the arc length: s = r \theta . r and \theta are the same as before. s is the arc length
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Apr 2008
    Posts
    1,092
    For the second question you also need the formula for arc length, which is s = r\theta, where s is the arc length, r is the radius, and \theta is the arc angle in radians. Edit: Jhevon beat me
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    769
    Hello, pyrosilver!

    As Jhevon suggested, make a sketch!


    Find the total grazing area of a goat.
    The animal is tied to the notheast corner of a 40' by 40' barn by an 80' rope.
    The south side of the barn is extended by a fence.
    Assume that there is grass everywhere except inside the barn.
    Code:
                  * * *
              *:::::|:::::*
            *:::::::|:::::::*
           *::::::::|80::::::*
           :::::::::|:::::::::
          *:::::::::|::::80:::*
          *----*----*---------*
          *::::| 40 |:::::::::*
            *::|    |::::::::*
        - - - -*- - * - - * - - - -

    The upper region is a semicircle with radius 80 feet.

    In the lower-left, there is a quarter-circle with radius 40 feet.


    In the lower-right, there is a strange-shaped piece.
    Code:
        A * - - - - - - - - * D
          |   *     80      *
       40 |       *
          |       30 *    *
        B * - - - - - - - * C
                40√3

    Right triangle ABC has side 40 and hypotenuse 80.

    From elementary Trig, \angle ACB = 30^o = \angle DAC
    . . and hence: BC = 40\sqrt{3}

    \Delta ABC has base 40\sqrt{3} and height 40.

    Sector ADC has \frac{1}{12} of the area of a circle with radius 80.


    I assume you can find those separate areas ... and add them.

    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Sep 2008
    Posts
    61
    OK I got it now, ty!
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,909
    Thanks
    769
    Hello again, pyrosilver!

    A 16-inch chord is drawn is a circle with a radius of 10 inches.

    (a) What is the angular size of the minor arc of the chord?
    Code:
                  * * *
              *     |  8  *
           A* - - - C - - - *B
           *  \     |     /  *
                \   |   /10
          *       \ |θ/       *
          *         *         *
          *         O         *
    
           *                 *
            *               *
              *           *
                  * * *

    In right triangle BCO\!:\;\;OB = 10,\;BC = 8

    Let \theta = \angle COB

    Then: . \sin\theta \:=\:\frac{8}{10} \quad\Rightarrow\quad \theta \:=\:\sin^{-1}(0.8) \:=\:0.927295218 radians

    Therefore: . \angle AOB \;=\;2\theta \;\approx\;1.8546 radians




    (b) What is the length of arc (nearest tenth)?

    \text{arc}\,AB \;=\;r\theta \;=\;10(1.8546) \;\approx\;18.5 inches.

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the Angles
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: May 3rd 2011, 10:02 AM
  2. Find point with two angles
    Posted in the Trigonometry Forum
    Replies: 11
    Last Post: February 14th 2011, 12:23 AM
  3. find the missing angles
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: November 23rd 2010, 07:51 AM
  4. Find All Three Angles
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: September 12th 2008, 05:28 AM
  5. Find the angles
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: November 11th 2007, 04:37 AM

Search Tags


/mathhelpforum @mathhelpforum