In a right-angled triangle MKE, angle K = 90 °, KE = 8cm, ME = 16cm, KD-height. Find the cut length KD-?

1. Using the formula of the Pythagorean theorem, we calculate the length of the leg MK:

MK = √ME ^ 2 – KE ^ 2 = √16 ^ 2 – 8 ^ 2 = √256 – 64 = √192 = √64 x 3 = 8√3 cm.

2. The length of the leg KE, located opposite the angle M, is equal to half the length of the hypotenuse AC

(AC / AB = 8: 16 = 1/2). Therefore, the angle M is equal to 30 ° (according to the properties of a right-angled triangle).

3. In the ICD triangle, the CD leg is opposite an angle of 30 °. Hence, its length is equal to half the length of the MK hypotenuse:

CD = MK: 2 = 8√3: 2 = 4√3 cm.

Answer: the length of the CD is 4√3 cm.