Question

in triunghiul ABC, se dau AB=BC=2 si AC=2 radical din 2. sa se determine cos A

Answer 1

$\mathrm{Observam~ca~AB^2+BC^2=2^2+2^2=4+4=8~si~AC^2=8.~Deci } \\ \mathrm{AB^2+BC^2=AC^2 \Rightarrow triunghiul~este~dreptunghic~in~B~\Rightarrow} \\ \mathrm{\Rightarrow m(\ \textless \ A)=m(\ \textless \ C)=45 \textdegree.} \\ \\ \cos A=cos~45 \textdegree =\frac{ \sqrt{2} }{2}.$