In a triangle abc, the angle C is 90 * AB = 6, tgA = √3. Find the AC.

First way.
Since tgBAC = √3, the angle BAC = arctan√3 = 600.
The sum of the acute angles of a right-angled triangle is 600, then the angle ABC = 90 – 60 = 300.
The AC leg lies against an angle of 300, then AC = AB / 2 = 6/2 = 3 cm.
Second way.
tgBAC = √3 = BC / AC, then let BC = X cm, AC = X * √3 cm.
By the Pythagorean theorem, AB ^ 2 = BC ^ 2 + AC ^ 2.
36 = X ^ 2 + 3 * X ^ 2.
4 * X ^ 2 = 36.
X ^ 2 = 9.
X = BC = 3 cm.
Answer: The length of the BC leg is 3 cm.