a: góc C=180-30-45=180-75=105 độ
b: b=3
=>AC=3
AB/sinC=AC/sinB=BC/sinA
=>AB/sin105=3/sin45=BC/sin30
=>\(AB=\dfrac{3+3\sqrt{3}}{2}\left(cm\right);BC=\dfrac{3\sqrt{2}}{2}\left(cm\right)\)
c: \(S_{ABC}=\dfrac{1}{2}\cdot AB\cdot AC\cdot sinA=\dfrac{9\sqrt{6}+9\sqrt{2}}{16}\left(cm\right)\)
\(\dfrac{1}{2}\cdot AH\cdot BC=\dfrac{9\sqrt{6}+9\sqrt{2}}{16}\)
=>\(AH=\dfrac{3+3\sqrt{3}}{4}\left(cm\right)\)
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