Answer: CD = 12.7
Step-by-step explanation:
Use Pythagorean Theorem or 30-60-90 rules to find that BC = 6√3
We know that ∠D = 55°, the opposite side (BC) = 6√3, and we are looking for the hypotenuse (CD).
[tex]sin\ \theta=\dfrac{opposite}{hypotenuse}\\\\\\sin\ 55^o=\dfrac{6\sqrt3}{CD}\\\\\\\text{cross multiply to get:}\\\overline{CD}\cdot sin\ 55^o=6\sqrt3 \\\\\\\text{divide sin 55 from both sides to get:}\\\overline{CD}=\dfrac{6\sqrt3}{sin\ 55^o}\\\\.\qquad=12.68\\\\\\\text{rounded to 3 significant digits we get:}\\\overline{CD}=12.7[/tex]
