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![](https://rs.olm.vn/images/avt/0.png?1311)
\(BC=\sqrt{3^2+4^2}=5\)
\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}\Rightarrow AH=\dfrac{12}{5}cm\)
\(AD=\sqrt{bc\left(1-\left(1-\dfrac{a}{b+C}\right)^2\right)}=\dfrac{4\sqrt{3}}{7}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
b: \(AH\cdot\left(\cot\widehat{B}+\cot\widehat{C}\right)\)
\(=AH\cdot\left(\dfrac{BH}{AH}+\dfrac{CH}{AH}\right)\)
\(=AH\cdot\dfrac{BC}{AH}=BC\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(AH^2=HB\cdot HC\)
\(\Leftrightarrow HC=\dfrac{4.8^2}{3.6}=6.4\left(cm\right)\)
Áp dụng hệ thức lượng trong tam giác vuông vào ΔABC vuông tại A có AH là đường cao ứng với cạnh huyền BC, ta được:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC\\AC^2=CH\cdot BC\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB^2=36\\AC^2=64\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}AB=6\left(cm\right)\\AC=8\left(cm\right)\end{matrix}\right.\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(\widehat{C}=60^0\)
\(AC=6\sqrt{3}\left(cm\right)\)
\(BC=12\sqrt{3}\left(cm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: Áp dụng định lí Pytago vào ΔABC vuông tại A, ta được:
\(BC^2=AB^2+AC^2\)
\(\Leftrightarrow AC^2=5^2-3^2=16\)
hay AC=4
Xét ΔBAC vuông tại A có
\(\sin\widehat{B}=\dfrac{AC}{BC}=\dfrac{4}{5}\)
nên \(\widehat{B}\simeq53^0\)
\(\Leftrightarrow\widehat{C}=37^0\)
b: Xét ΔABC có
BD là đường phân giác ứng với cạnh AC
nên \(\dfrac{AD}{AB}=\dfrac{CD}{BC}\)
hay \(\dfrac{AD}{3}=\dfrac{CD}{5}\)
mà AD+CD=4
nên Áp dụng tính chất của dãy tỉ số bằng nhau, ta được:
\(\dfrac{AD}{3}=\dfrac{CD}{5}=\dfrac{AD+CD}{3+5}=\dfrac{1}{2}\)
Do đó: AD=1,5cm; CD=2,5cm
Lời giải:
a. $\widehat{C}=90^0-\widehat{B}=90^0-60^0=30^0$
$\frac{AB}{BC}=\cos B=\cos 60^0$
$\Rightarrow BC=\frac{AB}{\cos 60^0}=\frac{8}{\cos 60^0}=16$ (cm)
$AC=\sqrt{BC^2-AB^2}=\sqrt{16^2-8^2}=8\sqrt{3}$ (cm)
b.
$AH=\frac{2S_{ABC}}{BC}=\frac{AB.AC}{BC}=\frac{8.8\sqrt{3}}{16}=4\sqrt{3}$ (cm)
$BH=\sqrt{AB^2-AH^2}=\sqrt{8^2-(4\sqrt{3})^2}=4$ (cm) theo định lý Pitago
Theo tính chất tia phân giác:
$\frac{BD}{DC}=\frac{AB}{AC}=\frac{8}{8\sqrt{3}}=\frac{1}{\sqrt{3}}$
$\Rightarrow \frac{BD}{BC}=\frac{1}{1+\sqrt{3}}$
$\Rightarrow BD=\frac{BC}{1+\sqrt{3}}=\frac{16}{1+\sqrt{3}}=-8+8\sqrt{3}$ (cm)
$HD=BD-BH=-12+8\sqrt{3}$
$AD=\sqrt{AH^2+HD^2}=\sqrt{(4\sqrt{3})^2+(-12+8\sqrt{3})^2}=7,17$ (cm)
Hình vẽ:
![](data:image/png;base64,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)