Question

sa se calculeze catatele ab si ac ale triunghiului Abc știind ca sin(b)=3/5 si bc=15

Answer 1

$\displaystyle\\ \text{Se da:}\\\\ \Delta ABC~ \text{ dreptunghic cu }~ m(\sphericalangle A)=90^o\\\\ \sin B =\frac{3}{5}\\\\ BC= 15~cm\\\\ \text{Se cere:}\\ \text{Lungimea catetelor AB si AC}\\\\ \text{Rezolvare:}\\\\ \text{Cateta AC este opusa unghiului B.}\\\\ \Longrightarrow~AC=BC\sin B=15\cdot\frac{3}{5}=\frac{15\cdot 3}{5}= \frac{45}{5}=\boxed{\bf 9~cm}\\\\ \text{Cateta AB o calculam cu teorema lui Pitagora.}\\\\ AB = \sqrt{BC^2-AC^2}=\sqrt{15^2-9^2}=\sqrt{225-81}=\sqrt{144}= \boxed{\bf 12~cm}$