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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Xét ΔABC có \(cosA=\dfrac{AB^2+AC^2-BC^2}{2\cdot AB\cdot AC}\)
=>\(8^2+12^2-BC^2=2\cdot8\cdot12\cdot\dfrac{1}{2}\)
=>\(BC^2=64+144-96=64+48=112\)
=>\(BC=4\sqrt{7}\left(cm\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(\widehat{A}=90^0\Rightarrow\Delta ABC\) vuông tại \(A\)
\(a,\widehat{C}=90^0-\widehat{B}=30^0\\ AC=\tan B\cdot AB=\tan60^0\cdot8=8\sqrt{3}\left(cm\right)\\ BC=\dfrac{AB}{\sin C}=\dfrac{8}{\sin30^0}=16\left(cm\right)\\ b,S_{ABC}=\dfrac{1}{2}AB\cdot AC=\dfrac{1}{2}\cdot8\cdot8\sqrt{3}=32\sqrt{3}\left(cm^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Kẻ đường cao AH ứng với BC
Đặt \(AB=x\) với \(0< x< 12\Rightarrow AC=12-x\)
Đặt \(BH=y\Rightarrow CH=8-y\) (với \(0< y< 8\))
Trong tam giác vuông ABH ta có:
\(cosB=\dfrac{BH}{AB}\Rightarrow BH=AB.cosB=\dfrac{x}{2}\Rightarrow y=\dfrac{x}{2}\)
\(\Rightarrow CH=8-y=8-\dfrac{x}{2}\)
\(sinB=\dfrac{AH}{AB}\Rightarrow AH=AB.sinB=\dfrac{x\sqrt{3}}{2}\)
Áp dụng Pitago cho tam giác vuông ACH:
\(AC^2=AH^2+CH^2\Leftrightarrow\left(12-x\right)^2=\left(\dfrac{x\sqrt{3}}{2}\right)^2+\left(8-\dfrac{x}{2}\right)^2\)
\(\Leftrightarrow16x-80=0\Rightarrow x=5\)
\(\Rightarrow AC=12-x=7\)
Vậy \(AB=5cm,AC=7cm\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tam giác ABC vuông tại A, B=60.
⇒ Tam giác ABC là 1 nửa tam giác đều
⇒AB = \(\frac{BC}{2}\) =4cm.
AC=12‐4=8cm
Vậy AB=4cm
AC=8cm
Kẻ: \(AH\perp BC\).Đặt \(AB=2x\Rightarrow BH=x\Rightarrow AH=x\sqrt{3};HC=8-x\)
Áp dụng định lí Pi-ta-go có:
\(AC=\sqrt{\left(x\sqrt{3}\right)^2+\left(8-x\right)^2}=\sqrt{4x^2-16x+64}\)
Do \(AB+AC=12\Rightarrow2x+\sqrt{4x^2-16x+64}=12\)
Giải phương trình có x = 2,5
\(\Rightarrow AB=2x=2.2,5=5cm\)
Thay số vào tính được AC =))
![](https://rs.olm.vn/images/avt/0.png?1311)
Dựng AH vuông góc với BC, đặt AB = x, ta có : AH = x.sin B = x.sin60 = x.căn 3 / 2
HB = x.cos 60 = x/2 => HC = BC - HB = 8 - x/2 = (16 - x)/2
AC = 12 - AB = 12 - x
Trong tam giác vuông AHC : AH^2 + HC^2 = AC^2
hay (x. căn 3 /2)^2 + (16 - x)^2/4 = (12 - x)^2
<=> 3x^2 + (16 - x)^2 = 4(12 - x)^2
Giải phương trình này tìm được x = 5
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Tam giác ABC vuông tại A, B=60.
\(\Rightarrow\) Tam giác ABC là 1 nửa tam giác đều
\(\Rightarrow AB=\frac{BC}{2}\) =4; AC=12-4=8
Lời giải:
Kẻ $BH\perp AC$ với $H\in AC$
Xét tam giác $ABH$ ta có: $\frac{AH}{AB}=\cos A=\cos 60^0=\frac{1}{2}$
$\Rightarrow AH=AB.\frac{1}{2}=2,5$ (cm)
$\frac{BH}{AB}=\sin A=\sin 60^0=\frac{\sqrt{3}}{2}$
$\Rightarrow BH=\frac{5\sqrt{3}}{2}$ (cm)
$CH=AC-AH=8-2,5=5,5$ (cm)
Áp dụng định lý Pitago cho tam giác $BHC$
$BC=\sqrt{BH^2+CH^2}=\sqrt{(\frac{5\sqrt{3}}{2})^2+5,5^2}=7$ (cm)
Hình vẽ:
![](data:image/png;base64,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)