Find the sides of a rectangle if the diagonal is 20 and the angle between the diagonals is 50 degrees.

In the rectangle ABCD, AC and BD are diagonals; AC = BD = 20; point O – the point of intersection of the diagonals; <AOB = 50 °;

Triangle AOB is isosceles, which means <ABO = <BAO = (180 ° – 50 °): 2 = 65 °;

cos <ABO = AB / BD; AB = BD * cos <ABO;

sin <ABO = AD / BD; AD = BD * sin <ABO;

sin 65 ° ≈ 0.91; cos 65 ° ≈ 0.42;

AB = 20 * 0.42 ≈ 8.4;

AD = 20 * 0.91 ≈ 18.2.