Results 1 to 5 of 5

Math Help - bearings

  1. #1
    Newbie
    Joined
    Oct 2007
    From
    Bahamas
    Posts
    21

    bearings

    An attendant in a lighthouse receives a request for aid from a stalled aircraft located 15 miles due east of the lighthouse. The attendant contacts a second boat located 14miles from the lighthouse on a bearing of N23degreesW. What is the distance and the bearing of the rescue boat from the stalled craft?

    90-23=67 degrees

    a_____________b
    15miles east

    cos67=15miles(adj)
    14 miles(hyp)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,710
    Thanks
    629
    Hello, cocoknny!

    An attendant in a lighthouse receives a request for aid
    from a stalled aircraft located 15 miles due east of the lighthouse.
    The attendant contacts a second boat located 14 miles from the lighthouse
    on a bearing of N23W.
    What is the distance and the bearing of the rescue boat from the stalled craft?
    Code:
        B *
           *    *
            *         *
             *    :         *
              *23:               *
            14 *  :                     *                   :
                * :                             *           :
                 *:                                   *   θ :
                  * - - - - - - - - - - - - - - - - - - - - *
                  L                 15                      A

    The lighthouse is at L. .The stalled aircraft is at A.;\;LA = 15

    The rescue boat is at B.\;\;BL = 14,\;\angle BLA = 113^o


    We want the distance AB and the bearing \angle\theta.


    Law of Cosines: . AB^2<br />
;=\;14^2 + 15^2 - 2(14)(15)\cos113^o \;=\;585.107074

    . . Hence: . \boxed{AB \:\approx\:24.2\text{ miles}}


    Law of Sines: . \frac{\sin A}{14} \:=\:\frac{\sin113^o}{24.2}\quad\Rightarrow\quad\s  in A \:=\:0.532523469

    Hence: . \angle A \:\approx\:32.2^o\quad\Rightarrow\quad\boxed{\angl  e\theta \:=\:57.8^o}


    Therefore, B is 24.2 miles from A at a bearing of N57.8^oW

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by cocoknny View Post
    An attendant in a lighthouse receives a request for aid from a stalled aircraft located 15 miles due east of the lighthouse. The attendant contacts a second boat located 14miles from the lighthouse on a bearing of N23degreesW. What is the distance and the bearing of the rescue boat from the stalled craft?

    90-23=67 degrees

    a_____________b
    15miles east

    cos67=15miles(adj)
    14 miles(hyp)
    Hi,

    1. make a sketch (see attachment)

    2. use cosine rule to calculate the distance between the 2 crafts:

    d=\sqrt{15^2+14^2-2\cdot 14 \cdot 15 \cdot \cos(113^\circ)}

    3. use sine rule to calculate the bearing (\alpha is the angle between the bearing to the rescue boat and the bearing from the rescue boat to the stalled craft):

    \frac{\sin(\alpha)}{\sin(113^\circ)}=\frac{15}{d}

    Calculkate \alpha. You get the bearing by calculating:

    180^\circ - 23^\circ - \alpha

    (I use N = 0, E = 90, S = 180, W = 270)

    You should get b = 122.2 that means E32.2S
    Attached Thumbnails Attached Thumbnails bearings-rettungsboot.gif  
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2007
    From
    Bahamas
    Posts
    21

    hello

    thanks so much hun, i was gettin lil confused before
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2007
    From
    Bahamas
    Posts
    21

    hey

    lol, i didn't even do the cosine rule yet. i only did Pythagoras and fundamental trig identities. I guess i'll look in my textbook. Thanks for the assistance.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. bearings
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 3rd 2008, 07:31 PM
  2. bearings
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: June 3rd 2008, 10:39 AM
  3. Bearings Help
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 22nd 2008, 06:54 AM
  4. bearings
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: October 17th 2007, 08:04 PM
  5. bearings.. help
    Posted in the Trigonometry Forum
    Replies: 6
    Last Post: October 16th 2007, 02:41 PM

Search Tags


/mathhelpforum @mathhelpforum