Question

Fie DEF un triunghi cu DE=DF=4√6 cm.Daca Aria DEF=24cm^2,determinati masura unghiului F...urgenttt.Dau coroana

Answer 1

Consideram triunghiul DEF obtuzunghic si isoscel, DE = DF.

Evident, unghiul D este obtuz.

$\mathcal{A} =\dfrac{DE\cdot DF\cdot \sin D}{2} = \dfrac{4\sqrt6\cdot 4\sqrt6\ \cdot \sin D}{2} = 48 \cdot \sin D\ \ \ \ (1)$

$Dar,\ \mathcal{A} = 24\ \ \ (2) \\\;\\ (1),\ (2) \Rightarrow 48\cdot \sin D =24 \Rightarrow \sin D = \dfrac{24}{48} =\dfrac{1}{2} \Rightarrow m(\hat{D}) =150^0$

$\Delta {DFE} -isoscel\ \Rightarrow m(\hat{F}) = m(\hat{E}) = \dfrac{180^0-150^0}{2}= 15^0$