In a triangle ABC, the angle is C = 90 degrees, AB = 8√5, AC = 8. find tg A.

In a right-angled triangle, the tangent of an angle is the ratio of the opposite leg to the adjacent one.
In triangle ABC, the tangent of angle A will be the ratio of leg BC to leg AC:
tgА = ВC / АC.
Let’s find the length of the BC leg according to the Pythagorean theorem:
BC = √ (AB ^ 2 – AC ^ 2);
ВС = √ ((8√5) ^ 2 – 8 ^ 2) = √ (64 * 5 – 64) = √ (320 – 64) = √256 = 16 (conventional units).
Then: tgА = 16/8 = 2.
Answer: tgА = 2.