Question

Determinati lungimea laturi AC a triunghiului BC=4;B=PI/6;C=PI/3

Answer 1

[tex]\it m(\hat{B}) =\dfrac{\pi}{6}\ \ \ \ \ (1) \\ \\ \\ m(\hat{C}) =\dfrac{\pi}{3} \ \ \ \ \ (2) \\ \\ \\ (1),\ (2) \Rightarrow m(\hat{A}) =\dfrac{\pi}{2}[/tex]

Aplicăm teorema sinusurilor:

$\it \dfrac{AC}{sinB} = \dfrac{BC}{sinA} \Rightarrow AC = \dfrac{BC sinB}{sinA} =\dfrac{4\cdot sin{\dfrac{\pi}{6}}}{sin\dfrac{\pi}{2}} = \dfrac{4\cdot\dfrac{1}{2}}{1} = 2$