Question

Să se calculeze sin( C) al triunghiului ABC , știind că AB = 4 , AC = 2 radical (3) și m(B)=30​

Answer 1

$\mathcal{\triangle ABC :}\;\; \mathsf{Fie} \mathcal {\; AM \perp BC,\;M \in BC}$

$\left.\begin{aligned} \mathcal{\triangle\,AMB: \sphericalangle M= } \;90^{\circ}\\ \sphericalangle \mathcal{B = }\; 30^{\circ} \;\;\;\;\;\; \;\;\; \end{aligned} \right\} \Rightarrow \mathcal{\red{\sin( \sphericalangle B)=\dfrac{AM}{AB}} }$

$\Rightarrow \;\dfrac{1}{2}=\dfrac{\mathcal{AM}}{4} \Rightarrow \mathcal{AM}=\dfrac{4}{2}=2$

$\mathcal{\triangle ACM : \sphericalangle{M} =}\,90^{\circ} \mathcal{\Rightarrow \red{\sin(\sphericalangle{C})=\dfrac{AM}{AC}}}$

$\mathcal{\sin(\sphericalangle{C})}=\dfrac{2}{2\sqrt{3}} \Rightarrow \green{\boxed{\mathcal{\sin(\sphericalangle{C})=}\dfrac{\sqrt{3} }{3}}}$