Question

Fie ABCD un paralelogram de 96cm.Daca AB=16cm si BC=12cm determinatimasurile unghiului paralelogramului

Answer 1

[tex]\displaystyle \\ \texttt{Se da: } \\ A_{_{ABCD}} = 96~cm^2 \\ AB = 16 ~cm \\ BC = 12 ~cm \\ \\ Se~cere: \\ \texttt{Masurile unghiurilor paralelogramului.} \\ \\ Rezolvare: \\ \texttt{Folosim formula: } \\ A_{_{ABCD}} = AB \times BC \times sin(\widehat{ABC}) \\ In ~care~~~sin(\widehat{ABC})~~~ este necunoscuta. \\ \\ 16 \times 12 \times sin(\widehat{ABC}) = 96 \\ \\ sin(\widehat{ABC}) = \frac{96}{16 \times 12} = \frac{96}{192} = \frac{1}{2} [/tex]


[tex]\displaystyle \\ \Longrightarrow ~m(\widehat{ABC})=30^o \\ m(\widehat{ADC}) = m(\widehat{ABC}) = 30^o ~~~(fiind~unghiuri ~opuse.) \\ \\ m(\widehat{ABC}) +m(\widehat{BCD}) = 180^o ~~~(fiind~unghiuri ~alaturate.) \\ \\ \Longrightarrow ~m(\widehat{BCD})=180^o -m(\widehat{ABC}) = 180^o - 30^o = 150^o \\ \\ m(\widehat{BAD})=m(\widehat{BCD}) = 150^o~~~(fiind~unghiuri ~opuse.) [/tex]