Cho tam giac ABC vuông tại A có đường cao AH . Đặt BH= x (x > 0), hãy tính x đối suy ra độ dài các đoạn AH và AC nếu biết AB = 3cm, CH= 3,2cm Giúp nhanh cho mình với
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![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 1:
Áp dụng HTL trong tam giác vuông:
$AB^2=BH.BC$
$\Rightarrow BH=\frac{AB^2}{BC}=\frac{6^2}{10}=3,6$ (cm)
$CH=BC-BH=10-3,6=6,4$ (cm)
Tiếp tục áp dụng HTL:
$AH^2=BH.CH=3,6.6,4$
$\Rightarrow AH=4,8$ (cm)
$AC^2=CH.BC=6,4.10=64$
$\Rightarrow AC=8$ (cm)
Bài 2:
Áp dụng định lý Pitago:
$BC=\sqrt{AB^2+AC^2}=\sqrt{3^2+1^2}=2$ (cm)
$AH=\frac{2S_{ABC}}{BC}=\frac{AB.AC}{BC}=\frac{\sqrt{3}.1}{2}=\frac{\sqrt{3}}{2}$ (cm)
$BH=\sqrt{AB^2-AH^2}=\sqrt{3-\frac{3}{4}}=\frac{3}{2}$ (cm)
$CH=BC-BH=2-\frac{3}{2}=\frac{1}{2}$ (cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, HB = 1,8cm; CH = 3,2cm; AH = 2,4cm; AC = 4cm
b, AB = 65cm; AC = 156cm; BC = 169cm; BH = 25cm
c, AB = 5cm; BC = 13cm; BH = 25/13cm; CH = 144/13cm
![](https://rs.olm.vn/images/avt/0.png?1311)
Áp dụng định lý Py - ta - Go vào tam giác ABC vuông tại A có :
AC2 = BC2 - AB2
AC2 =
Ta có :
Mà :
⇒
⇔ AH =
a) Áp dụng pi ta go ta có : AB2 = AH2 + BH2 = 162 + 252 = 881
=> AB =
Lại có : BH.HC = AH2
<=> HC.25 = 162
<=> HC.25 = 256
<=> HC = 256 : 25 = 10,24
Ta có : BC = HC + BH = 10,24 + 25 = 35,24
Áp dụng bi ta go : AC2 = AH2 + HC2 = 162 + 10,242 = 360,8576
=> AC =
![](https://rs.olm.vn/images/avt/0.png?1311)
1: \(AC=\sqrt{25^2-20^2}=15\left(cm\right)\)
\(AH=\dfrac{AB\cdot AC}{BC}=\dfrac{15\cdot20}{25}=12\left(cm\right)\)
\(BH=\sqrt{20^2-12^2}=16\left(cm\right)\)
CH=BC-BC=9(cm)
2: \(BC=10cm\)
\(AC=5\sqrt{3}\left(cm\right)\)
\(AH=\dfrac{AB\cdot AC}{BC}=\dfrac{5\sqrt{3}}{2}\left(cm\right)\)
\(BH=\dfrac{AB^2}{BC}=\dfrac{5^2}{10}=2.5\left(cm\right)\)
CH=BC-BH=7,5(cm)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(a,\)Áp dụng hệ thức lượng trong tam giác vuông ABC ta có
\(BC^2=AB^2+AC^2\Rightarrow BC^2=3^2+4^2\Rightarrow BC=\sqrt{9+16}\)
\(\Rightarrow BC=5cm\)
\(AB^2=BH.BC\Rightarrow BH=\frac{AB^2}{BC}\Rightarrow BH=\frac{3^2}{5}=\frac{9}{5}cm\)
\(AC^2=CH.BC\Rightarrow CH=\frac{AC^2}{BC}\Rightarrow CH=\frac{4^2}{5}=\frac{16}{5}cm\)
\(AH^2=\frac{9}{5}.\frac{16}{5}\Rightarrow AH^2=\frac{144}{25}\Rightarrow AH=\sqrt{\frac{144}{25}}=\frac{12}{5}cm\)
\(b,\)
\(BC=BH+CH\Rightarrow BC=9+16\Rightarrow BC=25cm\)
\(AB^2=BH.BC\Rightarrow AB^2=9.25\Rightarrow AB=\sqrt{225}=15cm\)
\(AC^2=CH.BC\Rightarrow AC^2=16.25\Rightarrow AC=\sqrt{400}=20cm\)
\(AH^2=BH.CH\Rightarrow AH^2=9.16\Rightarrow AH=\sqrt{144}=12cm\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, HB = 1,8cm; CH = 3,2cm; AH = 2,4cm; BC = 5cm
b, AB = 15cm; AC = 20cm; AH = 12cm; BC = 25cm
![](https://rs.olm.vn/images/avt/0.png?1311)
Bài 2:
Ta có: \(\dfrac{AB}{AC}=\dfrac{5}{6}\)
\(\Leftrightarrow\dfrac{HB}{HC}=\dfrac{25}{36}\)
\(\Leftrightarrow HB=\dfrac{25}{36}HC\)
Ta có: HB+HC=BC
\(\Leftrightarrow HC\cdot\dfrac{61}{36}=122\)
\(\Leftrightarrow HC=72\left(cm\right)\)
hay HB=50(cm)
Lời giải:
Áp dụng HTL trong tam giác vuông:
$AB^2=BH.BC=BH(BH+CH)$
$\Leftrightarrow 3^2=x(x+3,2)$
$\Leftrightarrow x^2+3,2x-9=0$
$\Leftrightarrow (x-1,8)(x+5)=0$
$\Rightarrow x=1,8$ (do $x>0$)
Vậy $x=1,8$ (cm)
Hình vẽ:
![](data:image/png;base64,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)