Explicație pas cu pas:
<B = 90°
[tex]BC = 12 \sqrt{3} [/tex]
[tex] \sin(C) = \frac{ \sqrt{3} }{2} [/tex]
folosim formula:
[tex] \sin^{2} ( \alpha ) + \cos^{2} ( \alpha ) = 1[/tex]
[tex] = > \cos^{2} (C) = 1 - \sin^{2} (C) = 1 - \frac{3}{4} = \frac{1}{4} \\ \cos(C) = \sqrt{ \frac{1}{4} }[/tex]
[tex]= > \cos(C) = \frac{1}{2} [/tex]
[tex]\cos(C) = \frac{BC}{AC} = > \frac{BC}{AC} = \frac{1}{2} \\ = > AC = 2 \times 12 \sqrt{3} = 24 \sqrt{3} [/tex]
[tex]= > AC = 24 \sqrt{3}[/tex]
[tex]AB^{2} = AC^{2} - BC^{2} = {(24 \sqrt{3} )}^{2} - {(12 \sqrt{3})}^{2} = 1296 = > AB = \sqrt{1296} [/tex]
[tex]= > AB = 36[/tex]
[tex] \tan(C) = \frac{AB}{BC} = \frac{36}{12 \sqrt{3}} = \sqrt{3} [/tex]
[tex] = > \tan(C) = \sqrt{3} [/tex]
[tex] \cot(C) = \frac{BC}{AB} = \frac{12 \sqrt{3} }{36} = \frac{1}{ \sqrt{3} } = \frac{ \sqrt{3} }{3} [/tex]
[tex]= > \cot(C) = \frac{ \sqrt{3} }{3} [/tex]
