In a rhombus, the height dropped from the top of the obtuse angle is 8 cm, divides the base

| August 16, 2021 | education

In a rhombus, the height dropped from the top of the obtuse angle is 8 cm, divides the base in half. find the diagonals and corners of the rhombus.

Since the height BH divides the side AD in half, it is also the median of the triangle ABD, then it is possible in an isosceles triangle AB = BD, and since all sides of the rhombus are equal, the triangle ABD is equilateral and all of its internal angles are 60. The angle BAD = 60, and since the opposite angles of the rhombus are equal, and the sum of the adjacent ones is 180, then the angle BCD = 60, the angle ABC = ADC = 180 – 60 = 120.

In a right-angled triangle, we determine the length of the hypotenuse BD.

ВD = ВН / Sin60 = 8 / √3 / 2 = 16 / √3 cm.

AB = 16 / √3 cm.

BO = BD / 2 = 8 / √3 cm.

In a right-angled triangle ABO, AO ^ 2 = AB ^ 2 – BO ^ 2 = (16 / √3) ^ 2 – (8 / √3) ^ 2 = (256 – 64) / 3 = 64.

AO = 8 cm.

Answer: The angles of the rhombus are 60, 120, the lengths of the diagonals are 8 cm and 16 / √3 cm.



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