(1) directly use the stability of the triangle to get the answer;

(2) According to the meaning of the question, express the length of each line segment, then use Pythagorean theorem to express the length of DC, and then use the acute trigonometric function relationship to get the answer.

Answer:

Solution:

The mathematical principles of (1) small bed design and application are: triangle has stability;

So, the answer is: triangles are stable;

(2)

∫AB:BC = 1:4，

∴ Let AB=x and DC=y, then BC=4x and c "d" = Y. From the figure, we can get that BC "= 4x, then AC" = 3x tan∠CAD = AD "= 3x+Y, so AC 2+DC 2 = AD 2, that is, (5x).

So the answer is: 8/ 15.