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Math Help - sides of a triangle

  1. #1
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    sides of a triangle



    i know side AC = \sqrt{52}


    but thats as far as my brain will take me right now, thanks
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  2. #2
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    Hello,

    Quote Originally Posted by silencecloak View Post


    i know side AC = \sqrt{52}


    but thats as far as my brain will take me right now, thanks
    How much do you know about trigonometry ?

    \cos B=\frac{BC}{AB} \ \begin{array}{c} \leftarrow \text{adjacent} \\ \leftarrow \text{hypotenuse} \end{array} , considering triangle ABC.

    \cos B=\frac{\color{red}BD}{BC} \ \begin{array}{c} \leftarrow \text{adjacent} \\ \leftarrow \text{hypotenuse} \end{array} , considering triangle BCD.

    \implies \frac{\color{red}BD}{BC}=\frac{BC}{AB}

    Does it help you ?
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    Thank you i appreciate your help as always
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  4. #4
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    Hello, silencecloak!

    28. Find BD.

    Code:
                C
                *
               *|  *
              * |     *  12
             *  |        *
            *   |           *
           *    |              *
        A *  *  *  *  *  *  *  *  * B
                D        x
          : - - - - 14  - - - - - :
    There is a theorem which covers this very situation,
    . . but we don't need it.


    Let x \,=\,BD

    Since \Delta CDB \sim \Delta ACB\!:\;\;\frac{x}{12}\:=\:\frac{12}{14} \quad\Rightarrow\quad\boxed{ x \:=\:\frac{72}{7}}

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