The distance from the point of intersection of the diagonals of the rhombus to one of its sides is 11

univerkov | March 2, 2021 | education

The distance from the point of intersection of the diagonals of the rhombus to one of its sides is 11, and one of the diagonals of the rhombus is 44. Find the value of the obtuse angle of the rhombus.

1. The vertices of the rhombus – A, B, C, D. The diagonals AC and ВD intersect at point O. OH = 11 units – perpendicular to the AC side. ВD = 44 units.

2.AO = AC: 2 = 44: 2 = 22 units of measurement (the diagonals of the rhombus are divided by the point of intersection into two identical segments).

3. Sine ∠НAO = OH / AO = 11/22 = 1/2:

4.НAO = 30 °.

5. ∠А = 30 х 2 = 60 ° (the AC diagonal is the bisector ∠А).

6. ∠D = 180 – ∠A = 180 – 60 ° = 120 ° (according to the properties of the rhombus).

Answer: ∠D = 120 ° – obtuse angle of the rhombus.

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