In triangle ABC, angle c is 90, tgB = 9 / √19. Find cosA.

The tangent of the angle of a right-angled triangle is the ratio of the opposite leg to the adjacent leg, then:

tgABC = AC / BC = 9 / √19.

Let the length of the segment BC = √19 * X cm, then the length of the leg AC = 9 * X cm.

Using the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 81 * X ^ 2 + 19 * X ^ 2 = 100 * X ^ 2.

AB = 10 * X cm.

Determine the cosine of the angle BAC of a right-angled triangle ABC,

CosBAC = AC / AB = 9 * X / 10 * X = 0.9.

Answer: The cosine of angle A is 0.9.