The side of the rhombus is 20 and the acute angle is 60 degrees. The height of the rhombus dropped

| January 28, 2021 | education

The side of the rhombus is 20 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 is the length of the segment.

Consider the AВD triangle, in which the angle A = 60, and the sides AB = СD, since all sides of the rhombus are equal, which means that the triangle AВD is isosceles. If at least one of the angles of an isosceles triangle is 600, then this triangle is equilateral. The diagonals of the rhombus divide it into four equal triangles, which means that the ВDС triangle is equilateral.

The height drawn from the top of an equilateral triangle is also its median and divides the opposite side in half.

Then DН = CH = 20/2 = 10 m.

Answer: The length of the segment is 10 cm.



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