In triangle ABC AC = BC the height CH is 8 AB = 32 find tgA.

1. Triangle ABC is isosceles, as by the condition of the problem AC = BC. Consequently, the height of the CH is also the median and divides the side AB to which it is drawn into two identical segments AH and BH. AH = BH = AB: 2 = 32: 2 = 16 units.

2. Triangle ACH is rectangular, since the height of CH forms a right angle with the side AB, to which it is drawn.

3. Calculate the tangent ∠A, equal to the ratio of the opposite leg CH to the adjacent leg AH:

Tangent ∠A = CH: AH = 8: 16 = 1/2.

Answer: tangent ∠A = 1/2.