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

\(\cos B=\frac{AB}{BC}=0,8\)  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 \(\cot B=\frac{0,8}{0,6}\)

\(\Rightarrow\cot B=\frac{4}{3}\)

+) \(B+C=90^0\)

\(\Rightarrow\sin B=\cos C=0,6\)

\(\Rightarrow\cos B=\sin C=0,8\)

\(\Rightarrow\tan B=\cot C=0,75\)

\(\Rightarrow\cot B=\tan C=\frac{4}{3}\)

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

      \(\sin\widehat{B}\)= \(\frac{AC}{AB}\)=\(\frac{0,9}{1,5}\)= \(0,6\)

      \(\cos\widehat{B}\)= \(\frac{BC}{AB}\)=\(\frac{1,2}{1,5}\)= \(0,8\)

     \(\tan\widehat{B}\)= \(\frac{AC}{BC}\)= \(\frac{0,9}{1,2}\)= \(0,75\)

      \(\cot\widehat{B}\)= \(\frac{BC}{AC}\)= \(\frac{1,2}{0,9}\)= \(\frac{4}{3}\)

      \(\sin\widehat{C}\)= \(\cos\widehat{B}\)= \(0,8\)

      \(\cos\widehat{C}\)= \(\sin\widehat{B}\)= \(0,6\)

     \(\tan\widehat{C}\)= \(\cot\widehat{B}\)= \(\frac{4}{3}\)

      \(\cot\widehat{C}\)= \(\tan\widehat{B}\)= \(0,75\)

cos N=4/5

=>sin P=4/5

cos P=căn 1-(4/5)^2=3/5

tan P=4/5:3/5=4/3

cot P=1:4/3=3/4

XÉT \(\Delta ABC\)CÂN TẠI A

\(\Rightarrow\hept{\begin{cases}AB=AC\\\widehat{B}=\widehat{C}\end{cases}}\)

TA CÓ \(\widehat{A}+\widehat{B}+\widehat{C}=180^o\left(Đ/L\right)\)

THAY\(50^0+\widehat{B}+\widehat{C}=180^o\)

                      \(\widehat{B}+\widehat{C}=130^o\)

MÀ\(\widehat{B}=\widehat{C}\)

\(\Rightarrow\widehat{B}=\widehat{C}=\frac{130^o}{2}=65^o\)

TA CÓ \(\widehat{DBA}+\widehat{ABC}=180^o\left(KB\right)\)

\(\Rightarrow\widehat{DBA}=180^o-65^o=115^o\)

TA CÓ\(\widehat{ACE}+\widehat{ACB}=180^o\left(KB\right)\)

\(\Rightarrow\widehat{ACE}=180^o-65^0=115^o\)

XÉT \(\Delta ACE\)CÓ AC=CE (GT) =>\(\Delta ACE\)CÂN TẠI C 

\(\Rightarrow\widehat{CAE}=\widehat{AEC}=\frac{180^o-115^0}{2}=32,5^0\)

XÉT \(\Delta ABD\)CÓ AB=BD (GT) =>\(\Delta ABD\)CÂN TẠI B

\(\Rightarrow\widehat{DAB}=\widehat{ADB}=\frac{180^o-115^0}{2}=32,5^0\)

TA CÓ\(\widehat{DAB}+\widehat{BAC}+\widehat{EAC}=\widehat{DAE}\)

THAY\(32,5^o+50^0+32,5^0=\widehat{DAE}\)

       \(\Rightarrow\widehat{DAE}=115^0\)