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

Given: ABC – rectangle. treug .;

C = 90 °;

AB = 2 sqrt (41), AC = 8;

tg В -? °

Because ABC is rectangular. treug., then for it the ratios and dependencies between the angles and sides apply.

By the Pythagorean theorem, we calculate the length of the BC leg:

ВС = sqrt (AB ^ 2 – AC ^ 2) = sqrt ((2 sqrt (41)) ^ 2 – 8 ^ 2) = sqrt (4 * 41 – 64) = sqrt (100) = 10.

Angle B is acute. Let’s find the tangent of this angle. In rectangular. treug. the tangent of an acute angle is the ratio of the legs of the triangles opposite to this angle. to the adjacent.

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

Answer: the tangent of angle B is 0.8.