Triangle ACB rectangular, CD height. Find AD if CBA is 30 degrees, AB hypotenuse is 8cm.

1. The leg AC of the triangle ABC is opposite to ∠ABC, equal to 30 °. Therefore, in accordance with the properties of a right-angled triangle, its length is half the length of the hypotenuse:

AC = 1/2 AB = 4 centimeters.

2. BC = √AB² – AC² = √8² – 4² = √64 – 16 = √48 = 4√3 centimeters.

3. The height CD is the leg of a right-angled triangle BCD opposite to ABC equal to 30 °. Therefore, its length is 1/2 BC:

СD = 2√3 centimeters.

4. АD = √АС² – СD² = √4² – (2√3) ² = √16 – 12 = √4 = 2 centimeters.