Question

in triunghiul ABC se da a=2√7 ,c=6 si cos2B=1/7.Aflati b.

Answer 1

$\it cos2B=\dfrac{1}{7} \Rightarrow 2cos^2B-1=\dfrac{1}{7} \Rightarrow cos^2B= \dfrac{1}{2}\cdot\dfrac{8}{7} \Rightarrow cos^2B=\dfrac{4}{7} \Rightarrow \\ \\ \\ \Rightarrow cosB=\dfrac{2}{\sqrt7}$

Cu teorema lui Pitagora generalizată, rezultă:

$\it b^2=a^2+c^2-2ac\cdot cosB = 28+36-2\cdot2\sqrt7\cdot6\cdot\dfrac{2}{\sqrt7} \Rightarrow \\ \\ \\ \Rightarrow b^2 = 64- 48 \Rightarrow b^2=16\Rightarrow b=4cm$