The value of CD = 12.687
Step-by-step explanation:
From the triangle ABC,
[tex]AC^{2}= AB^{2}+ BC^{2}[/tex] ( by using Pythagoras theorem)
or, [tex]BC^{2}= AC^{2} - AB^{2}[/tex]
or, [tex]BC^{2}[/tex] = 144 - 36 = 108
BC = [tex]\sqrt{108}[/tex] = 6[tex]\sqrt{3}[/tex]
Now,
[tex]\frac{BC}{CD}[/tex] = sin 55
or, CD = BC / sin 55
= 6[tex]\sqrt{3}[/tex] / sin 55
=12.687
