The side of the rhombus is 30 and the acute angle is 60 degrees. the height of the rhombus dropped from

The side of the rhombus is 30 and the acute angle is 60 degrees. the height of the rhombus dropped from the top of the obtuse angle divides the side into two segments. what are the lengths of these segments?

According to the condition, the acute angles B and D at the vertices of the rhombus are 60, then the dimensions of the obtuse angles A and C of the rhombus are (360 – 60 – 60) / 2 = 120. Since the diagonal AC, drawn from an obtuse angle, divides this angle in half, then it divides the rhombus into two triangles ABC and ADC, in which all angles are 60, therefore these triangles are equilateral. In an equilateral triangle, the height CO, drawn from the vertex C, divides the opposite side AB in half. Then the segments AO and AO will be equal to 30/2 = 15 cm.