In the triangle ABC, the angle is C = 90 ° AB 2√41. AC = 8 find tgB.

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 B will be the ratio of the AC leg to the BC leg:
tgB = AC / BC.
Finds the length of the BC leg according to the Pythagorean theorem:
BC = √ (AB ^ 2 – AC ^ 2);
ВС = √ ((2√41) ^ 2 – 8 ^ 2) = √ (4 * 41 – 64) = √ (164 – 64) = √100 = 10 (conventional units).
Then:
tgB = 8/10 = 4/5.
Answer: tgB = 4/5 = 0.8.