In a parallelogram, the angle between the diagonals is 3 times the angle between the smaller diagonal and the larger side.
| January 27, 2021 | education
In a parallelogram, the angle between the diagonals is 3 times the angle between the smaller diagonal and the larger side. The height of the parallelogram is half of the smaller dioganal. Find the angle between the diagonals.
Let’s draw the height АН of the parallelogram and consider the right-angled triangle АНС.
By condition, AH = AC / 2, AC = 2 * AH, then SinACH = AH / AC = AH / 2 * AH = 1/2.
Angle ACН = arcsin (1/2) = 30.
By condition, the AOD angle = 3 * AСВ, then the AOD angle = 3 * 30 = 90.
The diagonals intersect at right angles, AВСD = rhombus.
Answer: The angle between the diagonals is 90.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
