Answer:
<BAC=<BAD=60° (ΔABD is an equilateral triangle (all sides are equal) so each angle measures 60°)
All the angles in a triangle add to 180, so for ΔABC, we can write <ABC=180-60-30=90. So ΔABC is a right angled triangle with hypotenuse AC.
sinA=opposite/hypotenuse
sin30=AB/AC
1/2=AB/AC
AC=2AB=2AD
AC=AD+DC
AD+DC=2AD
DC=AD
QED
