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  1. #1
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    find theta

    find theta without the use of the law of cosines

    see image attached
    Attached Thumbnails Attached Thumbnails find theta-untitled.png  
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  2. #2
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    Quote Originally Posted by calc123 View Post
    find theta without the use of the law of cosines

    see image attached
    Why can't you use the Cosine Rule?
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  3. #3
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    well my prof told me i didnt need to know that for the test. so im trying to solve it a diff way
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  4. #4
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    Hello, calc123!


    Find \theta without the use of the Law of Cosines.
    Code:
          |     x     A
        D + - - - - - o
          |         **
          |     5 * *
        y |     *  *
          | θ *   *
          | *    *
        B o     * 7
          |    *
          |   *
        3 |  *
          | *
          |*
        C o

    We have: . AB = 5,\;\;BC = 3,\;\;AC = 7

    Let: . AD = x,\;\;BD = y,\;\;\theta = \angle DBA


    \begin{array}{ccc}\text{In right triangle }ADB\!: & x^2+y^2 \:=\:5^2 & [1] \\ \\<br /> <br />
\text{In right triangle }ADC\!: & x^2 + (y+3)^2 \:=\:7^2 & [2] \end{array}

    Subtract [2] - [1]: . (y+3)^2 - y^2 \:=\:49 - 25 \quad\Rightarrow\quad 6y \:=\:15 \quad\Rightarrow\quad y \:=\:\frac{5}{2}

    Hence: . \cos\theta \:=\:\frac{\frac{5}{2}}{5} \:=\:\frac{1}{2}


    Therefore: . \theta \;=\;\frac{\pi}{3}\;\;(60^o)

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