The smaller side of the rectangle is 4 cm and makes an angle of 60 degrees with the diagonal. Find the diagonal of the rectangle.

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

AB = 4 cm.

2. Triangle AOB is isosceles, since the diagonals of the rectangle are equal at the point

intersections are divided into equal segments.

∠AOВ = ∠ABO.

3. Since the sum of the angles of this geometric figure is 180 °, the degree measure

each of them is equal to 60, that is, the triangle AOB is equilateral.

Therefore, AB = BO = AO = 4 cm.

Diagonals ВD = AC = 4 x 2 = 8 cm.

Answer: diagonal ВD = AC = 8 cm.