In a right-angled triangle ABC with a hypotenuse AC = 12 cm, with a height BD, angle A is 30 degrees Find CD and AD.

In a right-angled triangle ABC, the BC leg lies opposite the angle 30, then its length is equal to half the length of the AC hypotenuse.

BC = AC / 2 = 12/2 = 6 cm.

The sum of the acute angles of a right-angled triangle is 90, then the angle ACB = (90 – 30) = 60.

Since ВD is the height, the triangle ВСD is rectangular, in which the angle СD = (90 – 60) = 30.

The CD leg lies opposite an angle of 30, then CD = BC / 2 = 6/2 = 3 cm.

Then AD = AC – CD = 12 – 3 = 9 cm.

Answer: The segment CD is 3 cm, AD is 9 cm.