Câu `1:`

`a)` Xét `ΔABC` vuông tại `A:`

`BC^2=AB^2+AC^2`

`→BC=sqrt(AB^2+AC^2)=sqrt(7^2+9^2)=sqrt(130)`

`sin\hat{B}=(AC)/(BC)=9/sqrt(130)`

`cos\hat{B}=(AB)/(BC)=7/sqrt(130)`

`tan\hat{B}=sin\hat{B}/cos\hat{B}=9/7`

`cot\hat{B}=1/tan\hat{B}=7/9`

`sin\hat{C}=(AB)/(BC)=7/sqrt(130)`

`cos\hat{C}=(AC)/(BC)=9/sqrt(130)`

`tan\hat{C}=sin\hat{C}/cos\hat{C}=7/9`

`cot\hat{C}=1/tan\hat{C}=9/7`

`b)` Xét `ΔABC` vuông tại `A:`

`BC^2=AB^2+AC^2`

`→AB=sqrt(BC^2-AC^2)=sqrt(13^2-5^2)=12`

`sin\hat{B}=(AC)/(BC)=5/13`

`cos\hat{B}=(AB)/(BC)=12/13`

`tan\hat{B}=sin\hat{B}/cos\hat{B}=5/12`

`cot\hat{B}=1/tan\hat{B}=12/5`

`sin\hat{C}=(AB)/(BC)=12/13`

`cos\hat{C}=(AC)/(BC)=5/13`

`tan\hat{C}=sin\hat{C}/cos\hat{C}=12/5`

`cot\hat{C}=1/tan\hat{C}=5/12`