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

The cosine of any angle is equal to the ratio of the adjacent leg to the hypotenuse. In this example cos (B) = BC / AB. Since the triangle is rectangular (the angle (C) is 90 degrees), you can apply the Pythagorean theorem to find the hypotenuse AB. We get:
AB ^ 2 = BC ^ 2 + AC ^ 2;
AB ^ 2 = 2 ^ 2 + (4√6) ^ 2; (add 4 under the root sign)
AB ^ 2 = 4 + √ (16 * 6) ^ 2;
AB ^ 2 = 4+ √96 ^ 2;
AB ^ 2 = 4+ 96;
AB ^ 2 = 100;
AB = √100;
AB = 10.
Hence we can find cos (B):
cos (B) = BC / AB;
cos (B) = 4/10;
cos (B) = 1/5.
Or in decimal 0.2.
Answer: cos (B) = 1/5 or 0.2 decimal.