Câu 1:
${{c}^{2}}={{a}^{2}}+{{b}^{2}}-2ab.\cos C$
${{c}^{2}}={{\left( 2\sqrt{3} \right)}^{2}}+{{2}^{2}}-2.2\sqrt{3}.2.\cos 30{}^\circ $
${{c}^{2}}=4$
$c=2$
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Câu 2:
${{b}^{2}}={{a}^{2}}+{{c}^{2}}-2ac.\cos B$
${{5}^{2}}={{4}^{2}}+{{c}^{2}}-2.4.c.\cos 150{}^\circ $
${{c}^{2}}+4\sqrt{3}c-9=0$
$c=\sqrt{21}-2\sqrt{3}$
$S=\dfrac{1}{2}ac\sin B=\dfrac{1}{2}.4.\left( \sqrt{21}-2\sqrt{3} \right).\sin 150=\sqrt{21}-2\sqrt{3}$
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Câu 3:
$\cos \widehat{ABC}=\frac{B{{A}^{2}}+B{{C}^{2}}-A{{C}^{2}}}{2.BA.BC}=\frac{-1}{4}$
$\to \widehat{ABC}\approx 104{}^\circ 29'$
$\to $ câu $B$
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Câu 4:
${{m}_{a}}^{2}=\dfrac{A{{C}^{2}}+A{{B}^{2}}}{2}-\dfrac{B{{C}^{2}}}{4}$
${{m}_{a}}^{2}=\dfrac{{{2}^{2}}+{{6}^{2}}}{2}-\dfrac{{{5}^{2}}}{4}$
${{m}_{a}}^{2}=\dfrac{55}{4}$
${{m}_{a}}=\dfrac{\sqrt{55}}{2}$
$\to $ câu $B$
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Bài 5:
${{S}_{ABCD}}=2{{S}_{ABC}}=2.\dfrac{1}{2}a.b.\sin ABC=ab\sin ABC$
$\to $ câu $B$
