Answer:
[tex]CD = 12.6866616739cm[/tex]
[tex]CD \approx12.7cm[/tex]
Step-by-step explanation:
[tex]CB = a[/tex]
[tex]AB = b[/tex]
[tex]AC = c[/tex]
[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]
[tex] {a}^{2} = {c}^{2} - {b}^{2} [/tex]
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
[tex]a = \sqrt{ {12}^{2} - {6}^{2} } [/tex]
[tex]a = \sqrt{144 - 36} [/tex]
[tex]a = \sqrt{108} [/tex]
[tex]CB = \sqrt{108} [/tex]
[tex] \sin(D) = \frac{opposite}{hypotenuse} [/tex]
[tex] \sin(D) = \frac{CB}{CD} [/tex]
[tex] \sin(55) = \frac{ \sqrt{108} }{CD} [/tex]
[tex](CD) \sin(55) = \frac{ \sqrt{108} }{CD} (CD)[/tex]
[tex](CD) \sin(55) = \sqrt{108} [/tex]
[tex] \frac{(CD) \sin(55) }{ \sin(55) } = \frac{ \sqrt{108} }{ \sin(55) } [/tex]
[tex]CD = \frac{ \sqrt{108} }{ \sin(55) } [/tex]
[tex]CD = 12.6866616739cm[/tex]
[tex]CD \approx12.7cm[/tex]
