In the ABC triangle, the angle c is 90 degrees cosA is equal to 2 roots of 6/5. find cosB.

First way.
Let the length of the leg AC = 2 * √6 * X cm, then the length of the hypotenuse AB = 5 * X cm.
Then, according to the Pythagorean theorem, BC2 = AB2 – AC2 = 25 * X2 – 24 * X2 = X2.
BC = X cm.
Then CosABC = BC / AB = X / 5 * X = 1/5.
Second way.
In a right-angled triangle, the cosine of one acute angle is equal to the sine of another acute angle, then SinABC = CosBAC = 2 * √6 / 5.
Then: Cos2ABC = 1 – Sin2ABC = 1 – 24/25 = 1/25.
CosABC = 1/5.
Answer: The cosine of angle B is 1/5.