In triangle ABC, angle C = 90 degrees, CH height, ab = 26, tangent of angle A = 2/3. Find NA.

Since the tangent of angle A is 2/3, the length of the segment BC = 2 * X cm, and the length of the segment AC = 3 * X cm.

Then, in a right-angled triangle ABC, by the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2.

676 = 13 * X ^ 2.

X ^ 2 = 52.

X = 2 * √13 cm.

Then AC = 6 * √13 cm, BC = 4 * √13 cm.

Triangles ABC and AСН are similar in acute angle, then:

AB / AC = AC / AН.

AH = AC ^ 2 / AB = 468/26 = 18 cm