In triangle ABC, angle A = 90 degrees, angle B = 30 degrees, AB = 6 cm. Find the sides of the triangle.

The ABC triangle is rectangular.
Let the length of the AC side be x cm.
Because in a right-angled triangle, the side opposite to an angle of 30 ° is equal to half the hypotenuse, then BC = 2x cm.
By the Pythagorean theorem, we have BC ^ 2 = AC ^ 2 + AB ^ 2.
(2x) ^ 2 = x ^ 2 + 6 ^ 2;
4x ^ 2 = x ^ 2 + 36;
3x ^ 2 = 36;
x ^ 2 = 12;
| x | = 2√3;
x = 2√3 (cm) – side length of the speaker.
Find the side of the BC:
2 * 2√3 = 4√3 (cm).
Answer: the sides of the triangle are 2√3 cm, 6 cm and 4√3 cm.