Trigonometry

In △DCE, DC = CE = 6, m∠E = 53º. Find DE.
So I tried to use tan or cot but there isn't a 90 degree angle C is 74 i somehow got 7.22 but i can't really explain how.

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  1. since the triangle is isosceles,
    m∠D = m∠E = 53º
    so, m∠C = 74º

    so, (DE/2)/6 = sin(74/2)º
    DE/12 = sin37º
    DE = 12 sin37º = 7.22

    or, using the law of sines,
    DE/sin74º = 6/sin53º
    DE = 7.22

    or, using the law of cosines,
    DE^2 = 6^2+6^2 - 2*6*6 cos74º
    DE = 7.22

    As you can see, the key to this was getting angle C

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  2. Thank you!

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  3. Thanks so much

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