Question

Un triunghi ABC are AC=8cm si cosB=3√5/7.Sa se det. sinB,lungimea razei cercului circumscris triunghiului

Answer 1

$\it sin^2B = 1-cos^2B =1-\dfrac{45}{49} =\dfrac{4}{49} \Rightarrow sinB=\dfrac{2}{7}$

$\it \dfrac{AC}{sinB} =2R \Rightarrow R = \dfrac{AC}{2 sin B} =\dfrac{8}{2\cdot\frac{2}{7}} =\dfrac{8}{\dfrac{4}{7}} = 8\cdot\dfrac{7}{4} =14 cm$