cho tam giac ABC co cosB=0,8 ko tinh B hay tim ti luong giac cua gocC
cho tam giac ABC vuong tai A. Biet cos B = 0,8, hay tinh cac ti so luong giac cua goc C
\(\cos B=\frac{AB}{BC}=0,8\) mà \(\sin C=\frac{AB}{BC}=\Rightarrow\sin C=0,8\)
Theo bài ra ta có :
\(\sin C^2+\cos C^2=\frac{AB}{BC}^2+\frac{AC}{BC}^2\)
\(=\frac{\left(AB^2+AC^2\right)}{BC^2}\)
\(=\frac{BC^2}{BC^2}\)
\(=1\)
\(\Rightarrow\cos C^2=1-\sin C^2=1-0,8^2=0,36\)
\(\Rightarrow\cos C=0,6\)hoặc \(\cos C=-0,6\)( loại vì C là một góc nhọn )
\(\Rightarrow\cos C=0,6\)
\(\Rightarrow\tan C=\frac{0,8}{0,6}=\frac{4}{3};\cot C=\frac{0,6}{0,8}=0,75\)
Vậy : \(\cos C=0,6\); \(\tan C=\frac{4}{3}\)và \(\cot C=0,75\)
ta co : \(\sin^2B+\cos^2B=1\)
\(\Rightarrow\sin^2B=1-\cos^2B\)
\(\Rightarrow\sin^2B=1-\left(0,8\right)^2\)
\(\Rightarrow\sin^2B=1-0,64\)
\(\Rightarrow\sin^2B=0,36\)
\(\Rightarrow\sin B=0,6\)
ta co: \(\tan B=\frac{\sin B}{\cos B}\)hay \(\tan B=\frac{0,6}{0,8}\)
\(\Rightarrow\tan B=0,75\)
ta co : \(\cot B=\frac{\cos B}{\sin B}\)hay \(\cot B=\frac{0,8}{0,6}\)
\(\Rightarrow\cot B=\frac{4}{3}\)
+) \(B+C=90^0\)
\(\Rightarrow\sin B=\cos C=0,6\)
\(\Rightarrow\cos B=\sin C=0,8\)
\(\Rightarrow\tan B=\cot C=0,75\)
\(\Rightarrow\cot B=\tan C=\frac{4}{3}\)
1.viet ti so luong giac thanh ti so luong giac cua goc nho hon 45 độ
sin 60 độ, cos 63 độ, tan 52 độ, cot 81 độ
2. ve tam giac vuong ABC vuong tai A, góc B = a
a) tan α =2 b) sinα= \(\dfrac{3}{5}\)
3. cho tam giac vuong ABC vuong tai A, BC =10cm, cos B =0,8
a. tinh cac canh AB,AC
b. tinh ti so luong giac goc C
Bài 3:
a: cos B=0,8 nên AC/BC=4/5
=>AC=8cm
=>AB=6cm
b: sin C=cos B=4/5
cos C=3/5
tan C=4/3
cot C=3/4
Cho tam giac ABC vuong tai A ,,co AC la 2cm ,BC 15cm,AB 3cm ( tinh goc alpha )viet ti so luong giac cua goc alphal (lam tron den do)
Cho tam giac ABC vuong tai C,trong do AC= 0,9m, BC= 1,2. Tinh cac ti so luong giac cua goc B, tu do suy ra cac ti so luong giac cua goc A.
Cac bn giup mk vs nha👍👍
Hình bạn tự vẽ nhé !
* Ta có : AB2 = AC2 + BC2
AB2 = 0,9 + 1,2 = 2,1
==> AB ~ 1,5 (m)
sinB = AC/AB = 0,9/1,5 = 0,6
CosB= BC/AB = 1,2/1,5=0,8
tanB= AC/BC = 0,9/1,2=0,75
cotB= BC/AC=1,2/0,9=1,3
Ta có AC vg AB
\(BC^2\) = \(AC^2\)+ \(AB^2\)
Hay \(BC^2\) = \(0,9^2\)+ \(1,2^2\)
\(BC^2\)= \(2,25\)
=> \(BC\) = \(\sqrt{2,25}\) = \(1,5\)cm
\(\sin\widehat{B}\)= \(\frac{AC}{AB}\)=\(\frac{0,9}{1,5}\)= \(0,6\)
\(\cos\widehat{B}\)= \(\frac{BC}{AB}\)=\(\frac{1,2}{1,5}\)= \(0,8\)
\(\tan\widehat{B}\)= \(\frac{AC}{BC}\)= \(\frac{0,9}{1,2}\)= \(0,75\)
\(\cot\widehat{B}\)= \(\frac{BC}{AC}\)= \(\frac{1,2}{0,9}\)= \(\frac{4}{3}\)
\(\sin\widehat{C}\)= \(\cos\widehat{B}\)= \(0,8\)
\(\cos\widehat{C}\)= \(\sin\widehat{B}\)= \(0,6\)
\(\tan\widehat{C}\)= \(\cot\widehat{B}\)= \(\frac{4}{3}\)
\(\cot\widehat{C}\)= \(\tan\widehat{B}\)= \(0,75\)
Tam giac ABC vuong tai C cosA=5/3 tinh ti so luong giac cua b
Cos A sao > 1 đc bạn ơi . Bn xem lại đề ạ
Tl
Đề bài nỗi ròi
#Kirito
Tam giac ABC co chu vi bang 24 cm va cac canh a,b,c ti le voi 3,4,5 .
a) Tinh cac canh cua tam giac ABC
b) Tam giac ABC co phai la tam giac vuong hay khong ? Vi sao ?
Bai 1 giai tam giac ABC vuong tai A, biet
a/ AB = 6cm, \(\widehat{B}\) = 40
b/ AB= 10cm, \(\widehat{C}\) = 35
c/BC=32cm, AC = 20cm
d/ AB = 18cm, AC=21cm
Bai 2 Cho △ABC co AB=40cm , AC=58cm , BC=42cm
a/ △ ABC co phai la tam giac vuong hay k ? vi sao ?
b/ Ke duong cao BH cua tam giac . Tinh do dai BH ?
c/ Tinh ti so luong giac cua goc A
Bai 3 : Cho △ABC co AB=5cm , \(\widehat{B}\) =60 , \(\widehat{A}\) = 45
a/ tinh do dai BC va AC
b/ Tinh dien tich △ABC
Bai 1 giai tam giac ABC vuong tai A, biet
a/ AB = 6cm, ˆBB^ = 40
b/ AB= 10cm, ˆCC^ = 35
c/BC=32cm, AC = 20cm
d/ AB = 18cm, AC=21cm
Bai 2 Cho △ABC co AB=40cm , AC=58cm , BC=42cm
a/ △ ABC co phai la tam giac vuong hay k ? vi sao ?
b/ Ke duong cao BH cua tam giac . Tinh do dai BH ?
c/ Tinh ti so luong giac cua goc A
Bai 3 : Cho △ABC co AB=5cm , ˆBB^ =60 , ˆAA^ = 45
a/ tinh do dai BC va AC
b/ Tinh dien tich △ABC
cho tam giac ABC vuong tai A, duong phan giac trong cua goc B va gocC cat nhau tai I. Duong thang di qua C vuong goc voi BI cat AB tai D. cho AB=5, IC= can bac hai cua 6, TINH BC