In triangle ABC, angle C is = 90 degrees, BC = 20 degrees, tgA = 0.5. Find AC.

Consider the triangle ABC, <C = 90º, AB – hypotenuse, AC and BC – legs, BC = 20 cm, tg A = 0.5.
By definition of the tangent of the angle of a right-angled triangle, the tangent of the angle is equal to the ratio of the opposite leg angle to the leg adjacent to the angle:
tg A = BC / AC.
Let us express the AC leg from this expression and find its length:
AC = BC / tg A = 20 / 0.5 = 40 cm.
Answer: the length of the AC leg is 40 cm.