Question

In triunghiul ABC
AB=5
AC=7
BC=√39
Calculeaza valoarea unghiului A

Answer 1

Aplicam teorema cosinusului:

$BC^2=AB^2+AC^2-2AB*ACcosA \\ BC^2-AB^2-AC^2=-2AB*ACcosA \\ AC^2+AB^2-BC^2=2AB*ACcosA \\ \\ cosA=\dfrac{AC^2+AB^2-BC^2}{2AB*AC}=\dfrac{1}{2}\implies A=60\textdegree$