In triangle ABC, angle C is 90 °, tgA = 2√6. Find cosA

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

tgBAC = BC / AC = 2 * √6 / 1.

Let the length of the segment AC = X cm, then the length of the leg BC = 2 * √6 cm.

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

AB ^ 2 = AC ^ 2 + BC ^ 2 = X ^ 2 + 24 * X ^ 2 = 25 * X ^ 2.

AB = 5 * X cm.

Then: CosBAC = AC / AB = X / 5 * X = 1/5 = 0.2.