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Math Help - problem with triangular geometry

  1. #1
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    problem with triangular geometry

    referring to the attached figure:
    In \triangle ABC,
    D is mid-point of BC,
     <br />
\angle ABD = \angle DAC = x<br />
    angle ADB = 45^o

    Need desperate help to find the value of x. Thanks.
    Attached Thumbnails Attached Thumbnails problem with triangular geometry-ques-10.jpg  
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  2. #2
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    The triangles ABC, DAC are similar (equal angles). Deduce that AC = \sqrt2DC. Then apply the sine rule in triangle ADC to find that \sin x = 1/2.
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    Quote Originally Posted by Opalg View Post
    The triangles ABC, DAC are similar (equal angles). Deduce that AC = \sqrt2DC. Then apply the sine rule in triangle ADC to find that \sin x = 1/2.
    alright that sounds easy, so x = 30 degrees
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