Question

urgent va toooog la matematica

Answer 1

 

$\displaystyle\bf\\Se~da:\\\triangle ABC~dreptunghic~cu~\angle B=90^o~inscris~in~cercul~cu~R=8~cm.\\\angle A=30^o\\\\Se~cere:\\Cateta~AB=~?\\\\Explicatiie:\\Un~triunghi~dreptunghic~inscris~in~cerc\\are~ipotenuza~egala~cu~diametrul~cercului.\\\\Rezolvare:\\AC=D=2R=2\times8=16~cm\\\\Cateta~BC=\frac{AC}{2}=\frac{16}{2}=8~cm~~(fiind~cateta~opusa~unghiului~de~30^o) \\\\AB=\sqrt{AC^2-BC^2}=\sqrt{16^2-8^2}=\sqrt{256-64}=\sqrt{192}=\sqrt{64\times3}\\\\\boxed{\bf AB=8\sqrt{3}~cm}$