Find the diagonals of a rhombus with side 6 and apex angle of 60 degrees.

| January 15, 2021 | education

The diagonals of the rhombus, at the point of intersection, are halved and intersect at right angles. Then AO = CO, BO = DO, and triangle AOB is rectangular.
The diagonal of the rhombus whitens the angle at the apex in half, that is, it is its bisector, then the angle ВАО = ВAD / 2 = 60/2 = 30.
In a right-angled triangle AOB, the leg BO lies opposite an angle of 300, and therefore is equal to half the length of the hypotenuse. ВO = AB / 2 = 6/2 = 3 cm. Current as ВO = DO, then the diagonal ВD = 2 * ВO = 2 * 3 = 6 cm.
Then the AВD triangle is equilateral, and its height AO = a * √3 / 2, where a is the side of the triangle. Then AO = AB * √3 / 2 = 6 * √3 / 2 = 3 * √3 cm.
Diagonal blood pressure = 2 * AO = 2 * 3 * √3 = 6 * √3 cm.
Answer: The diagonals of the rhombus are 6 cm and 6 * √3 cm.



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.