ABCD rectangle angle BAC = 30 degrees, AC = 8 cm. Find BC.

Let a rectangle ABCD be given, in which the angle BAC = 30 degrees, the diagonal AC = 8 cm. To find the side BC, consider the triangle ABC. It is rectangular because the angle ABC of the rectangle is 90 degrees. It is the common angle for both shapes. The hypotenuse in the triangle is the diagonal of the AC rectangle. By the property of the side lying in a right-angled triangle opposite an angle of 30 degrees, we find that the corresponding leg will be equal to half of the hypotenuse:
BC = AC: 2;
BC = 8: 2;
BC = 4 (cm).
Answer: The side of the rectangle BC is 4 centimeters.