In triangle ABC, angle C = 90, BC = 5, tgA = 1 / 2√2, find AB.

1. We calculate the length of the AC leg through the tangent ∠A – the ratio of the BC leg (located opposite the specified angle) to the AC leg, which is a side of the specified angle (adjacent to it):

BC / AC = 1 / 2√2.

AC = 5 x 2√2 = 10√2 units of measurement.

2. We calculate the length of the hypotenuse AB. For the calculation, we use the Pythagorean theorem:

AB = √BC² + AC² = √ (5² + (10√2) ² = √25 + 200 = √225 = 15 units.

Answer: AB length is 15 units.