Câu 7: Cho DABC
vuông tại A , đường cao AH phân giác AD . Cho
BD = 15cm,
DC = 20cm.
Tính AB, AC, AH , AD
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1:
BC=15+20=35cm
AD là phân gíac
=>AB/BD=AC/CD
=>AB/3=AC/4=k
=>AB=3k; AC=4k
AB^2+AC^2=BC^2
=>25k^2=35^2
=>k=7
=>AB=21cm; AC=28cm
AH=21*28/35=16,8cm
\(AD=\dfrac{2\cdot21\cdot28}{21+28}\cdot cos45=12\sqrt{2}\left(cm\right)\)
2:
BC=căn 12^2+16^2=20cm
HB=AB^2/BC=12^2/20=7,2cm
HC=20-7,2=12,8cm
BÀI 1:
a)
· Trong ∆ ABC, có: AB2= BC.BH
Hay BC= =
· Xét ∆ ABC vuông tại A, có:
AB2= BH2+AH2
↔AH2= AB2 – BH2
↔AH= =4 (cm)
b)
· Ta có: HC=BC-BH
àHC= 8.3 - 3= 5.3 (cm)
· Trong ∆ AHC, có:
·
Bài 1:
a) Áp dụng hệ thức lượng ta có:
\(AB^2=BH.BC\)
\(\Rightarrow\)\(BC=\frac{AB^2}{BH}\)
\(\Rightarrow\)\(BC=\frac{5^2}{3}=\frac{25}{3}\)
Áp dụng Pytago ta có:
\(AH^2+BH^2=AB^2\)
\(\Rightarrow\)\(AH^2=AB^2-BH^2\)
\(\Rightarrow\)\(AH^2=5^2-3^2=16\)
\(\Rightarrow\)\(AH=4\)
b) \(HC=BC-BH=\frac{25}{3}-3=\frac{16}{3}\)
Áp dụng hệ thức lượng ta có:
\(\frac{1}{HE^2}=\frac{1}{AH^2}+\frac{1}{HC^2}\)
\(\Leftrightarrow\)\(\frac{1}{HE^2}=\frac{1}{4^2}+\frac{1}{\left(\frac{16}{3}\right)^2}=\frac{25}{256}\)
\(\Rightarrow\)\(\frac{1}{HE}=\frac{5}{16}\)
\(\Rightarrow\)\(HE=\frac{16}{5}\)
Ta có BC=BD+DC=20+15=35(cm)
Ta có AD là phân giác \(\widehat{BAC}\) nên \(\dfrac{AB}{AC}=\dfrac{BD}{DC}=\dfrac{15}{20}=\dfrac{3}{4}\)
\(\Rightarrow\dfrac{AB^2}{AC^2}=\dfrac{9}{16}\Rightarrow\dfrac{AB^2}{9}=\dfrac{AC^2}{16}\)
Áp dụng tính chất dãy tỉ số bằng nhau:
\(\Rightarrow\dfrac{AB^2}{9}=\dfrac{AC^2}{16}=\dfrac{AB^2+AC^2}{25}=\dfrac{BC^2}{25}=49\)
\(\Rightarrow\left\{{}\begin{matrix}AB=\sqrt{49\cdot9}=21\\AC=\sqrt{49\cdot16}=28\end{matrix}\right.\)
Áp dụng HTL trong tam giác: \(AC^2=CH\cdot BC\Leftrightarrow28^2=CH\cdot35\Leftrightarrow CH=22,4\Leftrightarrow BH=BC-CH=12,6\)
và \(AH^2=BH\cdot HC=22,4\cdot12,6=282,24\)
Mà \(CH=CD+DH\Leftrightarrow22,4=DH+20\Leftrightarrow DH=2,4\)
Xét tam giác AHD vuông tại H, theo định lí Pytago có
\(AD=\sqrt{AH^2+DH^2}=\sqrt{282,24+2,4^2}=\sqrt{288}=12\sqrt{2}\approx16,97\)
Tick nha bạn
a) Xét ΔHBA vuông tại H và ΔABC vuông tại A có
\(\widehat{HBA}\) chung
Do đó: ΔHBA\(\sim\)ΔABC(g-g)
b) 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:
\(\dfrac{1}{AH^2}=\dfrac{1}{AB^2}+\dfrac{1}{AC^2}\)
\(\Leftrightarrow\dfrac{1}{AH^2}=\dfrac{1}{15^2}+\dfrac{1}{20^2}=\dfrac{625}{90000}\)
\(\Leftrightarrow AH=12\left(cm\right)\)
Áp dụng định lí Pytago vào ΔABH vuông tại H, ta được:
\(AB^2=AH^2+BH^2\)
\(\Leftrightarrow BH^2=15^2-12^2=81\)
hay BH=9(cm)
Áp dụng định lí Pytago vào ΔAHC vuông tại H, ta được:
\(AC^2=AH^2+CH^2\)
\(\Leftrightarrow CH^2=AC^2-AH^2=20^2-12^2=256\)
hay CH=16(cm)
Lời giải:
Áp dụng tính chất tia phân giác:
$\frac{AB}{AC}=\frac{BD}{DC}=\frac{15}{20}=\frac{3}{4}$
$\Rightarrow AB=\frac{3}{4}AC$
$BC=BD+DC=35$ (cm)
Áp dụng định lý Pitago:
$AB^2+AC^2=BC^2$
$(\frac{3}{4}AC)^2+AC^2=35^2$
$\frac{25}{16}AC^2=35^2$
$\Rightarrow AC=28$ (cm)
$AB=\frac{3}{4}AC=21$ (cm)
$AH=\frac{AB.AC}{BC}=\frac{21.28}{35}=16,8$ (cm)
$BH=\sqrt{AB^2-AH^2}=\sqrt{21^2-16,8^2}=12,6$ (cm)
$HD=BD-BH=15-12,6=2,4$ (cm)
$AD=\sqrt{AH^2+HD^2}=\sqrt{16,8^2+2,4^2}=12\sqrt{2}$ (cm)
Hình vẽ:
![](data:image/png;base64,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)