Results 1 to 3 of 3

Math Help - Trigonometry

  1. #1
    Chuyin
    Guest

    Trigonometry

    You are the captain of a yacht, the Beauty . A sudden storm rises and when it passes, you are far off the course. You radio for help, two lighthouses reply. Point Avery reports that your direction is 138.44 degrees (north is 0 degrees) and the Point Carradine reports that your direction is 196.69 degrees (again, north is 0 degrees). After consulting your maps you learn that Point Carradine is at direction 72.04 degrees from Point Avery and the distance between them is 38.15 miles. What is your distance from both point?

    First I drew a triangle that had at the ship an angle of 72.04 degreees so I got mess up and want to do this problem but I dont know if it is good can you reply this?

    Thank you
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Don't post the same question to multiple forums.

    RonL
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    Quote Originally Posted by Chuyin
    You are the captain of a yacht, the Beauty . A sudden storm rises and when it passes, you are far off the course. You radio for help, two lighthouses reply. Point Avery reports that your direction is 138.44 degrees (north is 0 degrees) and the Point Carradine reports that your direction is 196.69 degrees (again, north is 0 degrees). After consulting your maps you learn that Point Carradine is at direction 72.04 degrees from Point Avery and the distance between them is 38.15 miles. What is your distance from both point?

    First I drew a triangle that had at the ship an angle of 72.04 degreees so I got mess up and want to do this problem but I dont know if it is good can you reply this?

    Thank you
    It is important here that you draw the figure first.

    Draw any vertical-horizontal crossline. Call the intersection point A, for Avery. Draw a ray or line from point A that is 138.44 degrees clockwise from the North side of the vertical axis. So this ray is in the 4th quadrant or in the southeast position.

    Then, from A again, draw another ray that is 72.04 degrees clockwise from the North side. This ray is in the first quadrant or northeast position. On this ray, mark point C, for Carradine, that is supposed to be 38.15 miles from point A.

    Then draw another vertical-horizontal crossline whose intersection is at point C. From this point C, draw a ray that is 196.69 degrees clockwise from the new North side. This 3rd ray should intersect the 1st ray. Call their intersection point as B. This B is supposed to be the position of your Beauty, the yacht.

    So we have a triangle ABC.
    We know the length of one side, the AC. AC = 38.15 miles.
    We are asked to find AB and BC.

    From the given directions we can get the interior angles of triangle ABC. With the 3 angles known, and that known one side, we can get the other two sides AB and BC by using the Law of Sines.

    angle A = 138.44 -72.04 = 66.40 degrees. -------**
    angle C = 90 -(90 -72.04) -(196.69 -180) = 90 -17.96 -16.69 = 55.35 deg --**
    angle B = 180 -66.40 -55.35 = 58.25 degrees -----***

    By Law of Sines,
    38.15/sin(58.25deg) = AB/sin(55.35deg) = BC/sin(66.40deg) --------****

    Hence,
    AB = [38.15/sin(58.25deg)]*sin(55.35deg) = 36.91 miles.
    BC = [38.15/sin(58.25deg)]*sin(66.40deg) = 41.11 miles.

    Therefore, you are 36.91 miles from Point Avery, and 41.11 miles from Point Carradine. ------------answer.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometry to Memorize, and Trigonometry to Derive
    Posted in the Trigonometry Forum
    Replies: 9
    Last Post: August 21st 2013, 12:03 PM
  2. How To Do Trigonometry For This...?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 10th 2009, 05:56 PM
  3. How To Do This Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: January 3rd 2009, 01:55 AM
  4. trigonometry
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 31st 2008, 08:06 PM
  5. Trigonometry
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: December 18th 2008, 04:40 PM

/mathhelpforum @mathhelpforum