The smaller side of the rectangle is 10cm and makes an angle of 60 degrees with the diagonal.

The smaller side of the rectangle is 10cm and makes an angle of 60 degrees with the diagonal. 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 = 10 cm.

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 this geometric figure is 180 °, the degree measure of each of them is 60 °, and its sides are equal:

AB = BО = AO = 10 cm.

Diagonals ВD = АС = 10 х 2 = 20 cm.

Answer: diagonals BD = AC = 20 cm.