Question

[Hồ Hữu Duyy]

  

Answer 1

[Nguyễn Đức Trí]

Áp dung công thức Hê-rông:

\(S_{ABC}=\sqrt[]{p\left(p-a\right)\left(p-b\right)\left(p-c\right)}\)

mà \(p=\dfrac{a+b+c}{2}=\dfrac{10+8+6}{2}=12\)

\(\Leftrightarrow S_{ABC}=\sqrt[]{12\left(12-10\right)\left(12-8\right)\left(12-6\right)}\)

\(\Leftrightarrow S_{ABC}=\sqrt[]{12.2.4.6}=24\)

Ta lại có  \(S_{ABC}=\dfrac{1}{2}.h_a.a\)

\(\Leftrightarrow h_a=\dfrac{2.S_{ABC}}{a}\)

\(\Leftrightarrow h_a=\dfrac{2.24}{10}=\dfrac{24}{5}\)

\(S_{ABC}=\dfrac{1}{2}bcsin\widehat{A}\)

\(\Leftrightarrow sin\widehat{A}=\dfrac{2.S_{ABC}}{bc}\)

\(\Leftrightarrow sin\widehat{A}=\dfrac{2.24}{8.6}=1\)

\(\Leftrightarrow\widehat{A}=90^o\)