In triangle ABC, angle C is 90 degrees AB = 2√41 AC = 8 find tg B

Since C = 90 °, the triangle is right-angled with hypotenuse AB and leg AC. Using the Pythagorean theorem, we find the leg BC:

BC ^ 2 = AB ^ 2 – AC ^ 2 = (2 * √41) ^ 2 – 6 ^ 2 = 164 – 64 = 100;

BC = √100 = 10.

Then, by definition of the tangent, it will be equal to the ratio of the legs:

tg (B) = AC / BC = 8/10 = 0.8.