Cho tam giác nhọn ABC có BC = a; AB = AC = b; các đường cao BD, CE cắt nhau tại H. Nối D với E. Tính DE theo a, b.
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NL
Nguyễn Lê Phước Thịnh
CTVHS
17 tháng 5 2021
a) Xét ΔAEB vuông tại E và ΔAFC vuông tại F có
\(\widehat{FAC}\) chung
Do đó: ΔAEB\(\sim\)ΔAFC(g-g)
Suy ra: \(\dfrac{AE}{AF}=\dfrac{AB}{AC}\)(Các cặp cạnh tương ứng tỉ lệ)
hay \(AE\cdot AC=AF\cdot AB\)(ĐPCM)
NL
Nguyễn Lê Phước Thịnh
CTVHS
17 tháng 5 2021
b)
Ta có: \(\dfrac{AE}{AF}=\dfrac{AB}{AC}\)(cmt)
nên \(\dfrac{AE}{AB}=\dfrac{AF}{AC}\)
Xét ΔAEF và ΔABC có
\(\dfrac{AE}{AB}=\dfrac{AF}{AC}\)(cmt)
\(\widehat{FAE}\) chung
Do đó: ΔAEF\(\sim\)ΔABC(c-g-c)
HN
1
NQ
Nguyễn Quốc Đạt
CTVVIP
29 tháng 5
a) Tính các góc của tam giác
Ta có: $BC^2 = 14^2 = 196$
$AB^2 + AC^2 = 4,5^2 + 13^2 = 20,25 + 169 = 189,25$
Vì: $BC^2 > AB^2 + AC^2$ nên $\widehat{A}$ là góc tù.
Áp dụng định lý cosin:
$\cos A = \dfrac{AB^2 + AC^2 - BC^2}{2 \cdot AB \cdot AC}$
$= \dfrac{20,25 + 169 - 196}{2 \cdot 4,5 \cdot 13}$
$= \dfrac{-6,75}{117}$
$\approx -0,0577$
Suy ra: $\widehat{A} \approx 93^\circ$
Áp dụng định lý cosin với góc $B$:
$\cos B = \dfrac{AB^2 + BC^2 - AC^2}{2 \cdot AB \cdot BC}$
$= \dfrac{20,25 + 196 -169}{2 \cdot 4,5 \cdot 14}$
$= \dfrac{47,25}{126}$
$\approx 0,375$
=> $\widehat{B} \approx 68^\circ$
Góc còn lại: $\widehat{C} = 180^\circ - 93^\circ - 68^\circ \approx 19^\circ$
Vậy: $\widehat{A} \approx 93^\circ,\ \widehat{B} \approx 68^\circ,\ \widehat{C} \approx 19^\circ$
b) Tính diện tích tam giác $ABC$
Nửa chu vi là: $p = \dfrac{4,5 + 14 + 13}{2} = 15,75$
Diện tích tam giác: $S = \sqrt{p(p-AB)(p-BC)(p-AC)}$
$= \sqrt{15,75(15,75-4,5)(15,75-14)(15,75-13)}$
$= \sqrt{15,75 \cdot 11,25 \cdot 1,75 \cdot 2,75}$
$\approx \sqrt{852,54}$
$\approx 29,2$
Vậy diện tích tam giác $ABC$ xấp xỉ: $29,2\ \text{đơn vị diện tích}$.
NL
Nguyễn Lê Phước Thịnh
CTVHS
10 tháng 5 2023
a: Xét ΔAKB và ΔAKC có
AB=AC
góc BAK=góc CAK
AK chung
=>ΔAKB=ΔAKC
ΔABC cân tại A
mà AK là phân giác
nên AK vuông góc CB
b: Xét ΔACB có
BM,AK là trung tuyến
BM cắt AK tại G
=>G là trọng tâm
c: BK=CK=18/2=9cm
=>\(AK=\sqrt{30^2-9^2}=3\sqrt{91}\left(cm\right)\)
=>\(AG=2\sqrt{91}\left(cm\right)\)
15 tháng 6 2022
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