So AB=2BE, angular bed =90 degrees,

Because angle B=30 degrees and BD=4 degrees,

So DE=BD/2=2,

In the right triangle BDE, we can get from the hook-and-throw theorem:

Root number 3 of BE=2

So AB=4S root number 3,

In triangle ABC, because angle C=90 degrees and angle B=30 degrees,

So AC = AB/2 = the root number 3 of 2.

25。 Proof: Because AD is the height of triangle ABC,

So the angle ADB=90 degrees,

And because AB= 10 and AD=8,

Therefore, from Pythagorean theorem, BD=6,

Because BC= 12,

So BC=2BD, point D is the midpoint of BC,

So AD is perpendicular bisector of BC,

So AB=AC,

So triangle ABC is an isosceles triangle.

26。 The front half of the cylinder expands into a rectangle with a length of 4 cm and a width of 3 cm.

The crawling route of ants is the diagonal of this rectangle.

So we can know from Pythagorean theorem that we must climb at least 5 cm.