As shown in the figure, in the triangle ABC, the angle ABC is 90 degrees and the angle c is 30 degrees. Rotate the triangle ABC counterclockwise around point a to the position of triangle ab'c ', and point B falls on AC The value of tancdb 'is?

As shown in the figure, in the triangle ABC, the angle ABC is 90 degrees and the angle c is 30 degrees. Rotate the triangle ABC counterclockwise around point a to the position of triangle ab'c ', and point B falls on AC The value of tancdb 'is?

As shown in the figure, in the △ ABC, the △ ABC is 90 ° and C = 30 ° in the △ ABC, the △ ABC is rotated counterclockwise around point a to the position of △ AB & 3535353535; 39; C 35353535; C 35\3535\35\35\\\\\\\\\\\\\\\\\\; Let AB = 1, then AB-Ab = 1, AC = AC \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\bb & # △ AC & # - 39; D & nbsp; ∽ B & # - 39; BD ∽ AC & # - 39 / B & # - 39; b = ad / B & # - 39; d = 2 and ab & # - 39; = 1, ∽ B & # - 39; d = 1 / 3 ∽ Tan ∠ C & # - 39; DB & # - 39; & nbsp; = B & # - 39; C & # - 39; B & # - 39; /B'D=(√3)/(1/3)=3√3

As shown in the figure, ab = AC, ∠ ABC = 36 ° in △ ABC, side AC rotates 60 ° counterclockwise around point a to the position of AD, make ∠ ace = 12 ° and intersect BD at point e to connect AE. Try to determine what triangle △ AEC is? Please give reasons

Delta AEC is an isosceles triangle. The reasons are as follows: connecting CD, ∵ AC rotates 60 ° counterclockwise around point a to the position of AD, ∵ ad = AC, ∠ CAD = 60 ° then ∵ ACD is an equilateral triangle, ∵ ECD = 72 °, ∵ AB = AC, ∵ ABC = 36 °, ∵ BAC = 108 °, ∵ DAB = 168 °, ∵ abd = ∵ ADB = 6 °, ∵ EDC = 54 ° and ∵ CED = 180 ° - ∵ EDC - ∵ DCE = 54 ° and ∵ CE = CD = AC, that is an isosceles triangle ．

It is known that in the triangle ABC, the angle c = 90 degrees, AC = 4, BC = 3, the moving point P starts from point a and moves along the direction AB to the end B at a speed of 5 / 4 units per second
At the same time, the moving point Q starts from point a and moves along the direction of AC to the terminal point C at the speed of 1 unit per second. Connect PC and BQ and intersect at point D. let the movement time of two points be t (0

(1) Similar to ∵ - ACB = 90 ° AB = ac2 + BC2 = 5 ∵ PA = 54t, AQ = t ∵ paab = aqbc = T4 ∵ - a = ∵ a ∵ Apq ∵ ABC (2) ∵ Apq ∵ ABC ∵ PQA = ∵ C = 90 ° pqbc = aqac ∵ PQ3 = T4 ∵ PQ = 34T ∵ CQ = 4-T ∵ s = 12 ∵ 8226; 34T ∵ 8226; (4-T) = - 38t2 + 32t (3) storage

D. E and F are the points of BC, AB and AC in triangle ABC, and AE = AF, be = BD, CF = CD, ab = 4 and AC = 3
BD.DC=6 Find the area of triangle ABC
BD times DC = 6

Let AE = x, be = ybd = be = yCd = 6 / BD = 6 / YCF = CD = 6 / y ------ (1) AF = AE = x ------ (2) because AB = AE + be = 4, AC = AF + CF = 3, that is, x + y = 4, x + (6 / y) = 3x = 4-y, substitute 4-y + (6 / y) = 3, 1-y + (6 / y) = 0, multiply both sides by yy-y & sup2; + 6 = 0y & sup2; - y-6 = 0 (Y-3) (y + 2) = 0y = 3, y = - 2