Question

Fie un triunghi dreptunghic abc cu m(a)=90°. Aflati masurile unghiurilor ascutite stiind ca ab=5 radical 3 si ac=15

Answer 1

[tex]\it\dfrac{ab}{ac}=\dfrac{5\sqrt3}{15} \Rightarrow \dfrac{b}{c} = \dfrac{\sqrt3}{3}\ \ \ \ (1) \\\;\\ Dar,\ \ tg B = \dfrac{b}{c}\ \ \ \ (2) \\\;\\ \\\;\\ (1), (2) \Longrightarrow tgB = \dfrac{\sqrt3}{3} \Longrightarrow m(\hat{B}) =60^o\Longrightarrow m(\hat{C}) =30^o[/tex]