27) 0.8

Let the centre of the circle be O.

Here is how the diagram should look like:

AO = CO = 10 cm

Since D is opposite B, BD is also a diameter of the circle, meaning:

BO = DO = 10 cm

We know that triangle ABC is a right-angled triangle. We can find out BC using Pythagoras theorem.

AC² = AB² + BC²

20² = 12² + BC²

400 – 144 = BC²

BC² = 256

BC = 16 cm

We know triangle DBC is also a right-angle triangle with the hypotenuse being AC.

sine∠BDC = __ Opposite __ = __BC__ = __16
__ Hypotenuse BD 20

16 ÷ 20 = 0.8