Explicație pas cu pas:
1)
[tex]Aria = \frac{AB\cdot AC\cdot \sin(A)}{2} \\ 7 = \frac{AB\cdot 2\cdot \sin(30)}{2} < = > 7 = AB\cdot \frac{1}{2} \\ = > AB = 14[/tex]
2)
[tex]Aria = \frac{AB\cdot AC\cdot \sin(A)}{2} \\ = \frac{2 \sqrt{3}\cdot \sqrt{3}\cdot \sin(60)}{2} = \frac{ 3\sqrt{3} }{2} [/tex]
3)
[tex]\sin(B) = \frac{b}{a} = > b = a\sin(B) \\ \sin(C) = \frac{c}{a} = > c = a\sin(C)[/tex]
[tex]S = \frac{b\cdot c}{2} = \frac{a\cdot \sin(B) \cdot a\cdot\sin(C)}{2} \\ = \frac{ {a}^{2} \cdot \sin(B) \cdot \sin(C)}{2} \\ [/tex]
[tex] = > {a}^{2}\cdot \sin(B) \cdot \sin(C) = 2\cdot S[/tex]
4)
AB = 3, AC = 4, BC = 5
AB² + AC² = 9 + 16 = 25 = 5² = BC²
=> ΔABC este dreptunghic
teorema înălțimii:
[tex]h = \frac{AB\cdot AC}{BC} = \frac{3\cdot4}{5} = > h = \frac{12}{5} \\ [/tex]
5)
[tex]Aria = \frac{AB\cdot BC\cdot \sin(B)}{2} \\ 6 = \frac{3\cdot8\cdot \sin(B)}{2} \\ \sin(B) = \frac{1}{2} = > B = 30[/tex]
