The side of the rhombus is 26 and the acute angle is 60 °. The height of the rhombus, dropped from the top of the obtuse angle, divides the side into two segments. Find the product of the lengths of these segments.
Consider a triangle ABH, in which the angle A = 60, BH is the height drawn to the side AD, then the angle AHB = 90, and the angle ABH = 180 – 90 – 60 = 30.
The leg AH, right-angled triangle ABH, is located opposite the angle 30, therefore it is equal to half of the hypotenuse. AH = AB / 2 = 26/2 = 13 cm.
In a rhombus, all sides are equal, then the segment DH = AD – AH = 26 – 13 = 13 cm.
The product of the segments AH * DH = 13 * 13 = 169.
Answer: The product of the segments is 169.
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.