Results 1 to 3 of 3

Math Help - [SOLVED] Sine and Cosine Rule

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    40

    [SOLVED] Sine and Cosine Rule

    To find the breadth of a river, an observer stands at a point B on one bank and notes a point A directly across on the opposite bank.

    He then measures a distance BC of 36m in AB produced, and next walks a distance CD of 120m at right angles to AC.

    He then finds that AC subtends an angle of 56 degrees 20 minutes. at D. Find the breadth of the river, and the angle which AB subtends at D.

    I am having trouble interpreting this question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,400
    Thanks
    1849
    Have you drawn a picture? You actually have two right triangles, ACD and BCD.

    And, because they are right triangles you don't need either the "sine rule" or "cosine rule".

    Call the distance across the river "x". Then the total distance AC is 36+ x meters. That is the leg of the right triangle ACD opposite angle D. The "near side" has length 120 m. Solve the equation \frac{x+ 36}{120}= tan(56^o 20').

    Call the angle that BC (NOT AB) subtends at D " \theta". Then it is an angle of right triangle BCD with "opposite" side of length 36 m and "near side" of length 120 m. tan(\theta)= \frac{36}{120}. Once you have solved that for \theta, the angle AB subtends at D is 56 degrees 20 minutes minus \theta.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    40
    Thanks. I got the answer
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sine and cosine rule?
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: May 12th 2010, 05:31 AM
  2. problem using sine and cosine rule
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 28th 2009, 01:49 AM
  3. Sine and Cosine rule
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: September 3rd 2009, 04:20 PM
  4. Sine/ Cosine Rule Problems
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 5th 2009, 07:42 PM
  5. sine and cosine rule help
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: June 2nd 2009, 11:40 AM

Search Tags


/mathhelpforum @mathhelpforum