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Math Help - trig with no calc

  1. #1
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    trig with no calc

    in triangle ABC, angle C =  (\frac{\pi}{6}) and the side opposite angle c, AB = 2

    I am asked to find the side adjacent to angle C.

    I know  (\frac{\pi}{6}) = 30 degrees, and can solve this easily with a calculator using tan but how do you solve for that side without one?

    Thanks
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  2. #2
    o_O
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    You should also know that \tan \left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} \: \text{ or } \: \frac{\sqrt{3}}{3}

    So: \frac{1}{\sqrt{3}} = \frac{\text{AB}}{\text{AC}}

    Assuming this is a right triangle ...
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  3. #3
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    Quote Originally Posted by o_O View Post
    You should also know that \tan \left(\frac{\pi}{6}\right) = \frac{1}{\sqrt{3}} \: \text{ or } \: \frac{\sqrt{3}}{3}

    So: \frac{1}{\sqrt{3}} = \frac{\text{AB}}{\text{AC}}

    Assuming this is a right triangle ...
    could you explain

    well,  tan = \frac{sin}{{cos}} =  \frac{\frac{1}{2}}{\frac{2}{\sqrt{3}}} = \frac{1}{2}*\frac{2}{\sqrt{3}} = \frac{2}{2\sqrt{3}} = \frac{1}{\sqrt{3}}

    ha

    thanks for the push
    Last edited by silencecloak; August 27th 2008 at 03:03 PM.
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  4. #4
    o_O
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    Do you know your unit circle? i.e. the sin, cos, tan values of certain angles and \frac{\pi}{6} should definitely be one of them.

    So, we have:
    \begin{array}{rcl}\displaystyle\tan \left(\frac{\pi}{6}\right) & = & \displaystyle\frac{\text{AB}}{\text{AC}} \\& & \\ \displaystyle \frac{1}{\sqrt{3}} & = & \displaystyle\frac{2}{\text{AC}} \end{array}
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