Results 1 to 2 of 2

Math Help - The Sine Rule

  1. #1
    Junior Member
    Joined
    Dec 2007
    Posts
    59

    The Sine Rule

    Hi everyone,

    This is what should be another easy question but I'm unsure if I'm overlooking a piece of information that's important. Its about the Sine rule:

    A camera operator is positioned in a cherry-picker whose arm is 26m long and inclined at 110degrees to the horizontal. He is filming a cyclist who is racing towards him at 72km/h. He starts to film when the cyclist is 120m from the base of the cherry-picker. Find a) the angle a (angle of the cameras view of the cyclist) when the camera operator starts filming, b)the angle a five seconds after he starts filming.

    Thanks heaps, I think I've missed something or maybe I need to manipulate the question somehow??

    Steve
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,706
    Thanks
    625
    Hello, Stevo_Evo_22!

    A camera operator is positioned in a cherry-picker whose arm is 26m long
    and inclined at 110 to the horizontal.
    He is filming a cyclist who is racing towards him at 72 km/h.
    He starts to film when the cyclist is 120m from the base of the cherry-picker.

    Find a) the angle \theta (angle of the camera's view of the cyclist)
    when the camera operator starts filming

    b) the angle \theta five seconds after he starts filming.
    Code:
        A * - - - - - - - - - - - H
           \  *   θ
            \     *
             \        *
              \           *
            26 \              *
                \                 *
                 \ 110           θ   *
                B * - - - - - - - - - - - * C
                              d
    Let \theta \,= \,\angle HAC \,= \,\angle ACB

    Let d = distance from the cyclist C to the base of the cherry-picker B.

    Note that: . \angle CAB \:=\:180^o - 110^o - \theta \:=\:70^o - \theta


    Law of Sines: . \frac{\sin\theta}{26} \:=\:\frac{\sin(70-\theta)}{d} \quad\Rightarrow\quad d\!\cdot\!\sin\theta \:=\:26\sin(70-\theta)

    . . d\!\cdot\!\sin\theta \:=\:26(\sin70\cos\theta - \cos70\sin\theta) \:=\:26\sin70\cos\theta - 26\cos70\sin\theta

    . . d\cdot\sin\theta \;+ \;26\cos70\sin\theta \;=\;26\sin70\cos\theta \quad\Rightarrow\quad \sin\theta(d \;+ \;26\cos70) \;=\;26\sin70\cos\theta

    . . \frac{\sin\theta}{\cos\theta} \:=\:\frac{26\sin70}{d + 26\cos70} \quad\Rightarrow\quad \tan\theta \;=\;\frac{26\sin70}{d + 26\cos70}


    (a) When d = 120\!:\;\;\tan\theta \;=\;\frac{26\sin70}{120 + 26\cos70} \;=\;0.18955338

    . . Therefore: . \theta \;\approx\;10.7^o



    (b) The cyclist's speed is: . 72\text{ km/hr} \:=\:72,000\text{ m/hr} \:=\:20\text{ m/sec}

    In 5 seconds, he travels 100 m . . . Hence: . d = 20

    Then: . \tan\theta \;=\;\frac{26\sin70}{20 + 26\cos70} \:=\:0.845616962

    . . Therefore: . \theta \;\approx\;40.2^o

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Sine Rule q
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 16th 2009, 05:25 PM
  2. Sine rule...
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 22nd 2009, 03:46 PM
  3. Sine rule!
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 13th 2009, 01:40 PM
  4. sine rule
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: March 13th 2009, 09:12 PM
  5. sine rule
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 19th 2006, 05:30 AM

Search Tags


/mathhelpforum @mathhelpforum