Question

ΔABC-Deptunghic
masura unghiului A=90 grade
masura unghiului B=30 grade
AB=18 cm
Perimetrul ΔABC=?

Answer 1

      
$cos \;30^o = \frac{ \sqrt{3} }{2} \\ \\ \frac{AB}{BC} = cos \;30^o \\ \\ \frac{18}{BC} = \frac{ \sqrt{3} }{2} \\ \\ BC= \frac{18}{ \frac{ \sqrt{3} }{2}} =18* \frac{ 2 }{\sqrt{3}}=\frac{ 18*2 }{\sqrt{3}}= \frac{36}{\sqrt{3}}=\frac{ 36 \sqrt{3}}{3}=12 \sqrt{3} \;cm \\ \\ AC = \frac{BC}{2} =\frac{12 \sqrt{3}}{2} = 6\sqrt{3} \;cm \;\;\;\;\;(\text{Deoarece este opusa unghiului de 30}^o)\\ \\ P = AB + BC + AC = 18+ 12 \sqrt{3} + 6\sqrt{3}=18+18\sqrt{3} \; cm$