In triangle ABC, angle C = 90 degrees. tgA = 1/4. Find tgB.

The tangent of an angle in a right-angled triangle is equal to the ratio of the opposite leg to the adjacent leg. The tangent of angle A is equal to the ratio of the opposite leg BC to the adjacent leg AC.

tg ∠ A = BC / AC = 1/4.

Let BC = 1x cm, and AC = 4x cm (since AC is 4 times larger than BC). Find the tangent of angle B:

tg ∠ B = opposite AC leg / adjacent BC leg;

tg ∠ B = AC / BC;

tg ∠ B = 4x / 1x;

tg ∠ B = 4/1;

tg ∠ B = 4.

Answer: 4