Question

În triunghiul DEF unghiul, unghiul D =90°,DE =8cm și sinF=0,8.Calculati perimetrul triunghiului

Answer 1

 

$\displaystyle\bf\\Se~da:\\\\\Delta D EF\\D=90^o\\DE=8cm\\sin F=0,8\\\\Se~cere:\\\\Perimetrul~\Delta D EF\\Vezi~desenul~atasat.\\\\Rezolvare:\\\\sin F=\frac{co}{ip}=\frac{DE}{EF}=0,8\\\\\frac{8}{EF}=0,8\\\\EF=\frac{8}{0,8}\\\\\boxed{\bf~EF=10}\\\\DF=\sqrt{EF^2-DE^2}=\sqrt{10^2-8^2}=\sqrt{100-64}=\sqrt{36}=\boxed{\bf~6~cm}\\\\\\P=DE+EF+DF=8+10+6=\boxed{\bf~24~cm}$