The smaller side of the rectangle is 34. The diagonals intersect at an angle of 60 degrees. find the diagonals of the rectangle.

1. A, B, C, D – the vertices of the rectangle. ∠АВ = 60 °. О is the point of intersection of the diagonals. AB = 34 units.

2. Triangle AOB – isosceles, since the diagonals of the rectangle are equal and at the point of intersection are divided into equal segments.

∠AOB = ∠ABO

3. Since the total value of the angles of the triangle is 180 °, the degree measure of each of them is 60 °, and its sides are equal:

AB = BО = AO = 34 units.

Diagonals ВD = АС = 34 х 2 = 68 units.