Question

Rezolvați triunghiul ABC dacă b=45grade c=60grade si ac=6cm va rog dau coroana

Answer 1

$\it \widehat A=180^o-(60^o+45^o)=75^o\\ \\ \\Th.\ \ sinusurilor\ \Rightarrow\ \dfrac{BC}{sinA}= \dfrac{AC}{sinB}= \dfrac{AB}{sinC} \Rightarrow \dfrac{BC}{sin75^o}= \dfrac{6}{sin45^o}= \dfrac{AB}{sin60^o} \Rightarrow$

$\it \Rightarrow \begin{cases} \it \dfrac{BC}{\dfrac{\sqrt6+\sqrt2}{4}}= \dfrac{6}{\dfrac{\sqrt2}{2}} \Rightarrow BC=\dfrac{6\cdot\dfrac{\sqrt6+\sqrt2}{4}}{\dfrac{\sqrt2}{2}}=\dfrac{3(\sqrt6+\sqrt2)}{\sqrt2}=3\sqrt3+3\\ \\ \\ \it \dfrac{6}{\dfrac{\sqrt2}{2}}=\dfrac{AB}{\dfrac{\sqrt3}{2}} \Rightarrow AB=\dfrac{6\cdot\dfrac{\sqrt3}{2}}{\dfrac{\sqrt2}{2}}=\dfrac{^{\sqrt2)}6\sqrt3}{\ \sqrt2}=\dfrac{6\sqrt6}{2}=3\sqrt6\end{cases}$