In a right-angled triangle abc, the angle with the straight line CH is the height AB = 15, cosA = 0.6. Find AH.

1. In a right-angled triangle ABC, the leg AC is adjacent to the angle at the apex A, AB is the hypotenuse. Their ratio is equal to the cosine of the angle A (0.6).
2. We calculate the length of the AC leg:
AC / AB = 0.6.
AC = AB x 0.6 = 15 x 0.6 = 9 centimeters.
3. In a right-angled triangle ACН, the AН leg is adjacent to the СAН corner. AC – hypotenuse. Their ratio is equal to the cosine of the angle СAН (0.6).
4. We calculate the length of the leg AH:
AH / AC = 0.6.
AH = AC x 0.6 = 9 x 0.6 = 5.4 centimeters.
Answer: the length of the segment AH is 5.4 centimeters.