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Math Help - Triangle find angles

  1. #1
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    Triangle find angles

    If a=7, b=4, c=9; Find the angles A, B and C. Give your answer in degrees to at least 3 decimal places.

    A=?
    B=?
    C=?
    Last edited by qbkr21; November 29th 2006 at 10:05 AM. Reason: I got the Answer Myself....
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  2. #2
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    Hello, qbkr21!

    Given three sides of a triangle, you need the Law of Cosines.

    You should be able to start with: . a^2\;=\;b^2 + c^2 - 2bc\cos A

    . . and write it in the form: . \cos A \;= \;\frac{b^2 + c^2 - a^2}{2bc}


    If a=7,\;b=4,\;c=9, find the angles A,\:B,\:C.
    Give your answer in degrees to at least 3 decimal places.

    To find angle A, use: . \cos A \:=\:\frac{b^2+c^2-a^2}{2bc}

    . . We have: . \cos A \;=\;\frac{4^2+9^2-7^2}{2(4)(9)} \;=\;\frac{48}{72}

    . . Hence: . A \;= \;\cos^{-1}\!\!\left(\frac{48}{72}\right)\;=\;48.1896851

    . . Therefore: . \boxed{A \:=\:48.190^o}


    To find angle B, use: . \cos B \:=\:\frac{a^2 + c^2 - b^2}{2ac}

    . . We have: . \cos B\;=\;\frac{7^2 + 9^2 - 4^2}{2(7)(9)} \;=\;\frac{114}{126}

    . . Hence: . B \;= \;\cos^{-1}\!\!\left(\frac{114}{126}\right) \;=\;25.2087653

    . . Therefore: . \boxed{B \:=\:25.209^o}


    To find angle C, subtract A and B from 180^o. **

    . . Therefore: . C \;=\;180^o - 48.190^o - 25.209^o\quad\Rightarrow\quad\boxed{C \:=\:106.601^o}


    ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~


    ** That is, if you trust your answers for A and B.


    To check, we can find C with: . \cos C \:=\:\frac{a^2+b^2-c^2}{2ab}

    We have: . \cos C \;=\;\frac{7^2+4^2-9^2}{2(7)(4)} \;=\;-\frac{16}{56}

    Then: . C \;=\;\cos^{-1}\!\!\left(-\frac{16}{56}\right)\;=\;106.6015496^o . . . close enough!

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  3. #3
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    Re:

    Soroban I really appreciate you help, but I already found the answers, however I need you to work you magic with the word problem I posted just before this problem.
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