Question

rezultatul pe care l am obtinut este 4 radical din 3
ex6666666​

Answer 1

Mai intai afla catetele triunghiului dreptunghic:

$sin(B)=\frac{cat. opusa}{ip}=\frac{AC}{BC}\\ \Rightarrow sin(30)=\frac{AC}{16}\\\Rightarrow \frac{1}{2} =\frac{AC}{16}\\\Rightarrow AC=8$

$cos(B)=\frac{cat. alaturata}{ip}=\frac{AB}{BC}\\ \Rightarrow cos(30)=\frac{AB}{16}\\\Rightarrow \frac{\sqrt{3} }{2} =\frac{AB}{16}\\\Rightarrow AB=8\sqrt{3}$

$Aria_{\triangle ABC}=\frac{AB\cdot AC}{2}=\frac{8\cdot 8\sqrt{3} }{2}=32\sqrt{3}$