Cho tam giác ABC vuông tại A ; AB = 30cm, AC = 40cm kẻ đường cao AH
a) Tính độ dài AH và HB
b) Tia phân giác của góc B cắt AC tại B. Tính độ dài AD và DC
(giúp mình vs ạ đag cần gấp)
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\(1,HC=\dfrac{AH^2}{BH}=\dfrac{256}{9}\\ \Rightarrow AB=\sqrt{BH\cdot BC}=\sqrt{\left(\dfrac{256}{9}+9\right)9}=\sqrt{337}\\ 2,BC=\sqrt{AB^2+AC^2}=10\left(cm\right)\\ \Rightarrow BH=\dfrac{AB^2}{BC}=6,4\left(cm\right)\\ 3,AC=\sqrt{BC^2-AB^2}=9\\ \Rightarrow CH=\dfrac{AC^2}{BC}=5,4\\ 4,AC=\sqrt{BC\cdot CH}=\sqrt{9\left(6+9\right)}=3\sqrt{15}\\ 5,AC=\sqrt{BC^2-AB^2}=4\sqrt{7}\left(cm\right)\\ \Rightarrow AH=\dfrac{AB\cdot AC}{BC}=3\sqrt{7}\left(cm\right)\\ 6,AC=\sqrt{BC\cdot CH}=\sqrt{12\left(12+8\right)}=4\sqrt{15}\left(cm\right)\)
Bài 1:
Xét ΔABC vuông tại A có
\(AB^2+AC^2=BC^2\)
hay \(AB=\sqrt{13}\left(cm\right)\)
Xét ΔABC vuông tại A có
\(\sin\widehat{B}=\dfrac{AC}{BC}=\dfrac{6}{7}\)
nên \(\widehat{B}=59^0\)
hay \(\widehat{C}=31^0\)
Bài 1:
Áp dụng định lí Pytago vào ΔABC vuông tại B, ta được:
\(AC^2=BC^2+AB^2\)
\(\Leftrightarrow AB^2=AC^2-BC^2=12^2-8^2=80\)
hay \(AB=4\sqrt{5}cm\)
Vậy: \(AB=4\sqrt{5}cm\)
Bài 2:
Áp dụng định lí Pytago vào ΔMNP vuông tại N, ta được:
\(MP^2=MN^2+NP^2\)
\(\Leftrightarrow MN^2=MP^2-NP^2=\left(\sqrt{30}\right)^2-\left(\sqrt{14}\right)^2=16\)
hay MN=4cm
Vậy: MN=4cm
Bài 1 :
- Áp dụng định lý pi ta go ta được :\(BA^2+BC^2=AC^2\)
\(\Leftrightarrow AB^2+8^2=12^2\)
\(\Leftrightarrow AB=4\sqrt{5}\) ( cm )
Vậy ...
Bài 2 :
- Áp dụng định lý pi ta go vào tam giác MNP vuông tại N có :
\(MN^2+NP^2=MP^2\)
\(\Leftrightarrow MN^2+\sqrt{14}^2=\sqrt{30}^2\)
\(\Leftrightarrow MN=4\) ( đvđd )
Vậy ...
1:
góc BAH+góc KAC=90 độ
góc BAH+góc ABH=90 độ
=>góc KAC=góc ABH
Xét ΔHBA vuông tại H và ΔKAC vuông tại K có
BA=AC
góc ABH=góc CAK
=>ΔHBA=ΔKAC
Lời giải:
a)
Áp dụng định lý Pitago:
$BC=\sqrt{AB^2+AC^2}=\sqrt{30^2+40^2}=50$ (cm)
$AH=\frac{2S_{ABC}}{BC}=\frac{AB.AC}{BC}=\frac{30.40}{50}=24$ (cm)
$BH=\sqrt{AB^2-AH^2}=\sqrt{30^2-24^2}=18$ (cm)
b)
Theo tính chất tia phân giác:
$\frac{AD}{DC}=\frac{AB}{BC}=\frac{30}{50}=\frac{3}{5}$
$\Rightarrow \frac{AD}{AC}=\frac{3}{8}$
$\Leftrightarrow \frac{AD}{40}=\frac{3}{8}$
$\Rightarrow AD=15$ (cm)
$DC=AC-AD=40-15=25$ (cm)
Hình vẽ:
![](data:image/png;base64,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)