In triangle ABC, angle C is 90 degrees, CH is height, angle A is 30 degrees, AB = 22 cm. Find AH

In a right-angled triangle ABC, the leg CB lies opposite the angle A = 30 °, which means it is equal to half the hypotenuse:
СB = 1 / 2АB = 1/2 * 22 = 11 cm.
By the Pythagorean theorem, we find the second leg AC:
AC = √ (AB² – CB²) = √ (484 – 121) = √363 = 11√3 cm.
Now consider a right-angled triangle AНC, write down the cosine of the angle A:
cos A = AH / AC, hence:
AH = cos A * AC = cos 30 ° * 11√3 = √3 / 2 * 11√3 = 33/2 = 16.5 cm.
Answer: AH = 16.5 cm.