Results 1 to 2 of 2

Math Help - The Ambiguous Case (law of sine/ cosine)

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    27

    The Ambiguous Case (law of sine/ cosine)

    need some help 3 probs. on setting up the pictures, etc. plz thxs!

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Nismo
    Quote Originally Posted by Nismo View Post
    need some help 3 probs. on setting up the pictures, etc. plz thxs!

    For question 1, I am assuming that the ship's speed of 16 mph is measured through the water - not relative to the earth.

    The vector law of addition (of velocities) states:
    The velocity of the ship relative to the earth ({_SV_E}) = the velocity of the ship relative to the water ({_SV_W}) + the velocity of the water relative to the earth ({_WV_E}).
    Study the attached diagram carefully. It shows these three velocity vectors, drawn with the two possible directions of the current - that is, the velocity of the water relative to the earth.

    Using the Sine Rule:
    \frac{\sin\theta}{16}=\frac{\sin 15}{14}
    This gives the value of \theta (and 180-\theta). From this you can work out the two directions the current makes with the North. (If my arithmetic is correct, they are 32^o and 178^o, to the nearest degree.)

    In question 2, you need to draw a similar diagram, but this time you'll find there is only only possibility because the triangle is right-angled. See the second of the attachments. Since it's a right-angle triangle, it's very simple to work out the length of the third side to give the ground speed of the ship (that's the speed relative to the earth).

    Lastly, look at my third diagram to see the two different possibilities. Find \theta (and 180-\theta) using the Sine Rule. Then you can either (a) find the third angle and then use the Cosine Rule on each triangle to find the distances along the ground, or (b) possibly easier, because it just uses right-angled triangles, find the height above ground of the top of the pole (the dotted line in my diagram) and then the horizontal distances.

    Can you finish all these now?

    Grandad
    Attached Thumbnails Attached Thumbnails The Ambiguous Case (law of sine/ cosine)-untitled.jpg   The Ambiguous Case (law of sine/ cosine)-untitled2.jpg   The Ambiguous Case (law of sine/ cosine)-untitled3.jpg  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ambiguous Case Help
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 4th 2011, 09:30 AM
  2. Solution of triangles ambiguous case.
    Posted in the Trigonometry Forum
    Replies: 0
    Last Post: December 3rd 2011, 06:55 PM
  3. Ambiguous case using law of sines
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 30th 2011, 01:42 PM
  4. The Ambiguous Case...Two Solutions
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: September 13th 2008, 11:41 PM
  5. The Ambiguous Case...One Solution
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 13th 2008, 09:17 PM

Search Tags


/mathhelpforum @mathhelpforum