Question

In triungiul ABC , avem m(A) = 90 si tg (C) = 2. Aflati sin B

Answer 1

Folosim formula $cos^2x=\dfrac{1}{1+tg^2x}$ si obtinem:

$cos^2C=\dfrac{1}{1+tg^2C}=\dfrac{1}{5}\Rightarrow cosx=\dfrac{\sqrt5}{5}$

Deoarece unghiurile B si C sunt complementare, $sinB=cosC=\dfrac{\sqrt5}{5}$