The diagonal of the rectangle is 8 cm and the angle between the diagonals is alpha, find the sides of the rectangle.

Given:
ABCD – rectangle,
AC = BD = centimeters,
AC intersects with BD at point O,
angle BOС = a.
Find the sides: AD = BC, AB = CD -?
Decision:
1) The diagonals of the rectangle are halved by the intersection point. that is, ВO = OD = AO = OС = 4 centimeters;
2) Consider the BOС triangle. By the cosine theorem:
ВС ^ 2 = BO ^ 2 + OC ^ 2 – 2 * BO * OC * cosa;
BC ^ 2 = 4 ^ 2 + 4 ^ 2 – 2 * 4 * 4 * cosa;
ВС ^ 2 = 16 + 16 – 32 * cosa;
ВС ^ 2 = 32 – 32 * cosa;
3) Consider the BOA triangle. By the cosine theorem:
BA ^ 2 = BO ^ 2 + AO ^ 2 – 2 * BO * aC * cos (180 – a);
ВA ^ 2 = 4 ^ 2 + 4 ^ 2 + 2 * 4 * 4 * cosa;
ВA ^ 2 = 16 + 16 – 32 * cosa;
BA ^ 2 = 32 + 32 * cosa.
Answer: AD = BC = √ 32 – 32 * cosa, AB = CD = √ 32 + 32 * cosa.