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Calculati lungimea laturii AB a triunghiului ABC,dreptunghic in A,stiind ca BC=3 radical din 2 si masura unghiului B=45`grade.

Răspuns :

   
[tex]\displaystyle\\ \Delta ABC~\text{este dreptunghic si are un unghi de }45^o.\\\\ \Longrightarrow ~~\Delta ABC ~\text{este triunghi dreptunghic-isoscel.}\\\\ \texttt{Se da:}\\ m(\sphericalangle A)= 90^o\\ BC = 3 \sqrt{2} ~cm = ipotenuza\\ m(\sphericalangle B)= 45^o\\\\ \texttt{Se cere:}\\ AB = cateta = ? [/tex]


[tex]\displaystyle\\ \text{Rezolvare:}\\\\ \cos(B) = \frac{AB}{BC} \\\\ \Longrightarrow ~~ AB = BC\times\cos(B)= BC \times cos(45^o) = \\\\ =3\sqrt{2} \times \frac{ \sqrt{2} }{2}= \frac{3\sqrt{2} \times \sqrt{2} }{2}= \frac{3 \times 2 }{2}= \boxed{\bf 3~cm}[/tex]



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