In triangle ABC: angle C = 90, BC = 2, AC = 4 √6. Find the cos of angle B.

Triangle ABC is rectangular since the angle is C = 90.

To determine the cosine of angle B, you need to know the adjacent leg and the hypotenuse. The leg adjacent to the corner B is the well-known leg BC = 2, and the hypotenuse AB can be calculated based on the Pythagorean theorem (the square of the hypotenuse of a right triangle is equal to the sum of the squares of the legs).

AB ^ 2 = AC ^ 2 + BC ^ 2.

AB ^ 2 = (4 (6 ^ 1/2)) ^ 2 + 2 ^ 2 = 96 + 4 = 100.

Where, AB = 10.

cos B = 2/10 = 0.2.

Answer: in triangle ABC, the cosine of angle B is 0.2.