In an isosceles triangle ABC with a base AC, the lateral side AB is equal to 20 and cosA = 2√6 / 5.

In an isosceles triangle ABC with a base AC, the lateral side AB is equal to 20 and cosA = 2√6 / 5. Find the height drawn to the base.

Since BH is the height of triangle ABC, triangles ABH and BCH are rectangular.

In a right-angled triangle, the cosine of its acute angle is the ratio of the length of the adjacent leg to the length of the hypotenuse.

CosBAH = AH / AB.

AH = AB * CosBAH = 20 * 2 * √6 / 5 = 8 * √6 cm.

In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg BH.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 400 – 384 = 16.

BH = 4 cm.

Answer: The length of the height drawn to the base is 4 cm.