Question

sa se determine lungimea laturii AC a triunghiului ABC, daca AB=3, m(<C)=45° si m(<B)=30°

Answer 1

$\text{Folosim teorema sinusurilor:}\\ \dfrac{AB}{\sin C}=\dfrac{AC}{\sin B}\Rightarrow AC=\dfrac{\sin B\cdot AB}{\sin C}\\ AC=\dfrac{\frac{1}{2}\cdot 3}{\frac{\sqrt 2}{2}}=\dfrac{3}{\sqrt 2}=\boxed{\dfrac{3\sqrt 2}{2}}$