Question

Pls help I don’t understand this question very well

Answer 1

Answer:

$CD = 12.6866616739cm$

$CD \approx12.7cm$

Step-by-step explanation:

$CB = a$

$AB = b$

$AC = c$

${c}^{2} = {a}^{2} + {b}^{2}$

${a}^{2} = {c}^{2} - {b}^{2}$

$a = \sqrt{ {c}^{2} - {b}^{2} }$

$a = \sqrt{ {12}^{2} - {6}^{2} }$

$a = \sqrt{144 - 36}$

$a = \sqrt{108}$

$CB = \sqrt{108}$

$\sin(D) = \frac{opposite}{hypotenuse}$

$\sin(D) = \frac{CB}{CD}$

$\sin(55) = \frac{ \sqrt{108} }{CD}$

$(CD) \sin(55) = \frac{ \sqrt{108} }{CD} (CD)$

$(CD) \sin(55) = \sqrt{108}$

$\frac{(CD) \sin(55) }{ \sin(55) } = \frac{ \sqrt{108} }{ \sin(55) }$

$CD = \frac{ \sqrt{108} }{ \sin(55) }$

$CD = 12.6866616739cm$

$CD \approx12.7cm$