DC = 16
Explanation:
ABD is a right triangle (Angle ADB is a right angle)
Using the Pythagoras Theorem,
AB^2 = AD^2 + BD^2
AB^2 = 9^2 + 12^2
AB^2 = 81 + 144
AB^2 = 225
AB = 15
In triangle ABD,
sin(Angle A) = BD/AB
sin(Angle A) = 12/15
Angle A = sin^(-1)[12/15]
Angle A ≈ 53.13 degrees
In triangle ABC,
cos(Angle A) = AB/AC
cos(53.13) = 15/AC
AC = 15/cos(53.13)
AC ≈ 25
DC = AC - AD = 25 - 9 = 16
