Question

Помогите решить 2 вариант все задания

Answer 1

По теореме косинусов:

$displaystyleboxed{1}\\tt AC=sqrt{4^2+(3sqrt{2})^2-2cdot4cdot3sqrt{2}cdot frac{sqrt{2}}{2}} =sqrt{16+18-24} =sqrt{10} \\\ boxed{2}\\tt AC=sqrt{(2sqrt{3})^2+3^2-2cdot2sqrt{3}cdot3cdotbigg(-frac{sqrt{3}}{2}bigg)} =sqrt{12+9+18} =sqrt{39}$

По теореме синусов:

$displaystyleboxed{3}\\tt frac{AB}{sin C}= frac{AC}{sin B} Rightarrow AC=frac{ABcdotsin B}{sin C}=frac{4sqrt{2}cdotfrac{sqrt{3}}{2}}{ frac{sqrt{2}}{2}}=4sqrt{3}\\\ boxed{4}\\ angle{C}=180-(135+15)=30^o\\ AC=frac{ABcdotsin B}{sin C}=frac{4cdotfrac{sqrt{2}}{2}}{ frac{1}{2}}=4sqrt{2}$