Results 1 to 2 of 2

Math Help - Trig Ratios Right Triangles

  1. #1
    Newbie
    Joined
    Apr 2007
    Posts
    4

    Trig Ratios Right Triangles

    I was doing some homework in my math book and I'm having a hard time with these questions. Here is one that i don't have much idea to do with. Grade 11 University math thanks!

    Question 1:
    The arm of a boom crane is 12m long. Because of the location of the construction site, the angle of inclination of the boom of the crane has a minimum value of 30 degrees and a maximum of 45 degrees. Find the vertical displacement of the end of the boom as
    a) an exact value
    b) an approximate value, to the nearest tenth of a metre.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

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


    1) The arm of a boom crane is 12m long.
    Because of the location of the construction site, the angle of inclination
    of the boom of the crane has a minimum value of 30 and a maximum of 45.

    Find the vertical displacement of the end of the boom as
    a) an exact value
    b) an approximate value, to the nearest tenth of a metre.
    Code:
                            *
                         *  |
                 12   *     |
                   *        | y1
                *           |
             * 30          |
          * - - - - - - - - *
    You're expected to the ratio of the sides of a 30-60 right triangle.

    The side opposite the 30-angle is always one-half the hypotenuse.

    Hence: . (b)\;y_1 \,=\,6 m.



    Code:
                      *
                    * |
              12  *   |
                *     | y2
              *       |
            * 45     |
          * - - - - - *
    You should know that sides of a 45-45 right triangle are in the ratio: . 1:1:\sqrt{2}

    Hence: . y_2\:=\:\frac{12}{\sqrt{2}}\:=\:6\sqrt{2}


    Therefore: . (a)\;y_2 - y_1 \;=\;6\sqrt{2} - 6 \;=\;6(1-\sqrt{2})\;m

    . . . . . . . . (b)\;y_2-y_1 \;=\;2.485281376 \;\approx\; 2.5\;m


    .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding similar triangles using ratios
    Posted in the Geometry Forum
    Replies: 19
    Last Post: November 14th 2011, 10:17 AM
  2. Replies: 5
    Last Post: May 29th 2011, 03:10 PM
  3. A problem on triangles (area, ratios)
    Posted in the Geometry Forum
    Replies: 38
    Last Post: May 16th 2011, 04:32 AM
  4. Basic Trig Ratios - Circles, Tangents and Triangles
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 8th 2011, 04:52 PM
  5. Ratios of areas of triangles..
    Posted in the Geometry Forum
    Replies: 2
    Last Post: September 15th 2007, 08:04 PM

Search Tags


/mathhelpforum @mathhelpforum