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.