Question

Va rog ex 5,dau coroana!

Answer 1

Răspuns:

Explicație pas cu pas:

BC=12

Daca m(∡c)=30°⇒ AB=6 si 2AD=AC

Aplicam Pitagora in ΔABC

BC²=AB²+AC²

AC²=144-36=108

AC=6√3⇒ AD=3√3

$A_{ABC}=\frac{AB\cdot AC}{2} =\frac{6\cdot 6\sqrt{3} }{2} =18\sqrt{3}$

Aplicam in ΔABC teorema catetei

$AC^{2} =CD\cdot BC\\108=CD\cdot12\\CD=9$

$A_{ADC}=\frac{AD\cdot CD}{2} =\frac{3\sqrt{3} \cdot 9}{2} =\frac{27\sqrt{3} }{2}$

$A_{ABD}=A_{ABC}-A_{ABD}=18\sqrt{3} -\frac{27\sqrt{3} }{2} =\frac{9\sqrt{3} }{2}\\ \frac{A_{ABD}}{A_{ACD}} =\frac{9\sqrt{3} }{27\sqrt{3} } =\frac{1}{3}$