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Trịnh Việt Dũng
15 tháng 6 2022 lúc 20:31

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nguyễn hoàng lê thi
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Phạm Đỗ Anh
23 tháng 10 2018 lúc 23:02

Hạ đường cao AH của △ABC

⇒AH⊥BC

Vì △ABC nhọn

⇒Điểm H nằm giữa 2 điểm B và C

Diện tích △ABC là: SABC=\(\dfrac{1}{2}\).BC.AH(1)

Áp dụng hệ thức giữa cạnh và góc vào △AHB(H=900 ),ta có:

AH=AB.\(\sin B\)(2)

Từ (1) và (2)⇒SABC=BC.AB.\(\sin B\)(đpcm)

Akai Haruma
23 tháng 10 2018 lúc 23:18

Bài 1:
Kẻ đường cao $AH$ của tam giác $ABC$. Ta có:

\(\sin A=\frac{BH}{AB}\)

\(\frac{1}{2}BH.AC=S_{ABC}\Rightarrow BH=\frac{2S_{ABC}}{AC}\)

\(\Rightarrow \sin A=\frac{2S_{ABC}}{AB.AC}\)

\(\Rightarrow \frac{BC}{\sin A}=\frac{AB.AC.BC}{2_{ABC}}\)

Hoàn toàn tương tự, kẻ đường cao từ đỉnh $B,C$ , cuối cùng ta có:

\(\frac{BC}{\sin A}=\frac{AC}{\sin B}=\frac{AB}{\sin C}=\frac{AB.BC.AC}{2S_{ABC}}\)

Vậy ta có đpcm.

Akai Haruma
23 tháng 10 2018 lúc 23:21

Bài 2:

\(\cot a.\tan a=1\Rightarrow cot a=\frac{1}{\tan a}\). Thay vào pt đã cho ta có:

\(\tan a+\cot a=2\Leftrightarrow \tan a+\frac{1}{\tan a}=2\)

\(\Rightarrow \tan ^2a+1-2\tan a=0\)

\(\Leftrightarrow (\tan a-1)^2=0\Rightarrow \tan a=1\)

\(\Rightarrow a=\arctan (1)=\frac{\pi}{4}\) (radian) và bằng $45^0$

Vậy \(a=45^0\)

Hùng Nguyễn Đức
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Nguyễn Thị Hương
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Hải Yến Lê
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ging Hà
18 tháng 3 2021 lúc 11:53

J đây b

Phạm Phúc Tiến
19 tháng 12 2021 lúc 14:16

Chưa viết hết đầu bài kìa

Khách vãng lai đã xóa
Thành Nguyễn
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Nhật Văn
17 tháng 2 2023 lúc 18:43

Đề lỗi

Thành Nguyễn
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Nhật Văn
17 tháng 2 2023 lúc 18:43

Đề lỗi

Thành Nguyễn
17 tháng 2 2023 lúc 18:43

 đề đây nha mn :((   cho tam giác ABC nhọn (AB<AC) nội tiếp đường tròn (O;K) có BD là đường kính và đường cao AH của tam giác ABC cắt (O;K) tại E

Anh
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xuân quỳnh
23 tháng 8 lúc 10:03

=> Đề của bạn chưa đầy đủ và rõ ràng, bạn xem lại nhé!

TÍNH NGÔ
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TÍNH NGÔ
14 tháng 3 2023 lúc 21:54

Cho tam giác ABC nhọn AB<AC M là trung điểm của BC trên tia đời của tia MA có điểm E s cho AM=ME 
a) cmr tam giác AMB=CMR
b từ A kẻ D s cho HA =HD cmr CE = BP 
c cmr CE = CD tam giác AMD là tam giác j vì s 
D  CMR AM NHỎ HƠN AB +AC /2
​CHỈ LM MỖI Ý D THUI NHA NHANH NHA

Nguyễn Lê Phước Thịnh
14 tháng 3 2023 lúc 22:02

a: Xét ΔAMB và ΔEMC có

MA=ME

góc AMB=góc EMC

MB=MC

=>ΔAMB=ΔEMC

b: Xet ΔBAD có

BH vừa là đường cao, vừa là trung tuyến

=>ΔBAD cân tại B

=>BD=BA=CE

c: Xet ΔMAD có

MH vừa là đường cao,vừa là trung tuyến

=>ΔMAD cân tại M

d: AM<1/2(AB+AC)

=>AE<AB+AC

=>AE<BE+AB(luôn đúng)