Question

Answer 1

a) Ta có:

\(\widehat{A}+\widehat{B}+\widehat{C}=180^o\)

\(\Rightarrow\widehat{A}=180^o-30^o-45^o=105^o\)  

Áp dụng định lý sin ta có:

\(\dfrac{BC}{sinA}=\dfrac{AB}{sinC}\)

\(\Rightarrow AB=\dfrac{BC\cdot sinC}{sinA}=\sqrt{6}-\sqrt{2}\left(cm\right)\)

\(\dfrac{AB}{sinC}=\dfrac{AC}{sinB}\)

\(\Rightarrow AC=\dfrac{AB\cdot sinB}{sinC}=\dfrac{\left(\sqrt{6}-\sqrt{2}\right)\cdot sin45^o}{sin30^o}=2\sqrt{3}-2\left(cm\right)\) 

b) Diện tích tam giác ABC là:

\(S_{ABC}=\dfrac{1}{2}\cdot AB\cdot AC\cdot sinA=\dfrac{1}{2}\cdot\left(\sqrt{6}-\sqrt{2}\right)\cdot\left(2\sqrt{3}-2\right)\cdot sin105^o=\sqrt{3}-1\left(cm^2\right)\)