Răspuns:
[tex] \cos(B) = \frac{ \sqrt{3} }{2} [/tex]
Explicație pas cu pas:
[tex]AB = 4 \: \: \: \: \: \: AC = \sqrt{7} \: \: \: \: \: BC = \sqrt{3} [/tex]
[tex] \cos(B) =? [/tex]
[tex] {AC}^{2} = {AB}^{2} + {BC}^{2} - 2 \times AB \times BC \times \cos(B) \\ [/tex]
[tex]7 = 16 + 3 - 2 \times 4 \times \sqrt{3} \times \cos(B ) \\ [/tex]
[tex] - 12 = - 8 \sqrt{3} \times \cos(B) \: si \: acum \: scoatem \: \cos(B) \\ [/tex]
[tex] \cos(B) =scapam \: de \: - uri \: = \frac{12}{8 \sqrt{3} } = \frac{ 3}{2 \sqrt{3} } = \frac{3 \sqrt{3} }{2 \sqrt{3} \sqrt{3} } = \frac{3 \sqrt{3} }{6} = \frac{ \sqrt{3} }{2} \\ [/tex]
