Question

un triunghi isoscel abc are unghiul a de 150 de grade si latura ac de 36 cm. Cum aflu aria triunghiului?

Answer 1

   
[tex]\displaystyle\\ \begin{minipage} {3in} Enuntul nu spune care laturi ale triunghiului isoscel ABC sunt egale, dar faptul ca unghiul A este obtuz inseamna ca AB = AC. \end{minipage}\\\\\\ \text{In }\Delta ABC \text{ avem:}\\ \sphericalangle A = 150^o\\ AB = AC = 36~cm\\\\ \text{Calculam aria cu formula: } \boxed{A_{_{\Delta ABC}} = \frac{bc\,\sin A}{2}} [/tex]


[tex]\displaystyle\\ A_{_{\Delta ABC}} = \frac{AB\times AC\,\sin 150^o}{2} =\\\\ = \frac{AB\times AC\,\sin (180^o-30)}{2} = \\\\ = \frac{AB\times AC\,\sin (30)}{2} =\\\\ = \frac{36\times 36\times \dfrac{1}{2} }{2} =\frac{36\times 36}{4} =36\times 9 =\boxed{\bf 324~cm^2}[/tex]