Results 1 to 2 of 2

Math Help - Right triangle, find exact values w/sin addition formula

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    19

    Right triangle, find exact values w/sin addition formula

    Check out the attached pic with the triangles and their data. I started out finding the missing sides using Pythagorem Theorem. Then I used the Law of Cosines to find angles A and B. I need to find the exact value of sin(A+B), but doing this doesn't result in answers that can use an addition or subtraction formula to get a "nice" exact value from the unit circle.....I've been kicked around by this problem for the last 2 days!!! Am I going about this wrong? If so, could someone shed some light on this for me?

    Thanks,

    ~CC
    Attached Files Attached Files
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,814
    Thanks
    703
    Hello, calvin_coolidge!

    Find the exact value of \sin(A+B)
    Code:
          A
          *
          | *
          |   *  21           *
        5 |     *             |  *     __
          |       *         3 |     * √58
          |         *         |        *
          * - - - - - *       * - - - - - * B
              4√26                  7

    In the left triangle, the third side is: . \sqrt{21^2-5^2} \:=\:4\sqrt{26}

    . . Hence: . \begin{array}{ccc}\sin A &=& \dfrac{4\sqrt{26}}{21} \\ \\[-3mm] \cos A &=& \dfrac{5}{21} \end{array}


    In the right triangle, the hypotenuse is: . \sqrt{3^2+7^2} \:=\:\sqrt{58}

    . . Hence: . \begin{array}{ccc}\sin B &=& \dfrac{3}{\sqrt{58}} \\ \\[-3mm] \cos B &=& \dfrac{7}{\sqrt{58}} \end{array}


    Substitute into: . \sin(A+B) \;=\;\sin A\cos B + \sin B\cos A

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 2nd 2010, 02:41 PM
  2. Evaluate and find exact values
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 22nd 2009, 04:06 AM
  3. Find area of triangle [Heron's Formula]
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: January 11th 2009, 10:11 PM
  4. Find the exact values
    Posted in the Trigonometry Forum
    Replies: 5
    Last Post: July 10th 2008, 01:48 PM
  5. find exact values for theta
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: February 28th 2008, 04:00 PM

Search Tags


/mathhelpforum @mathhelpforum