The side of the rhombus is 32, and the acute angle is 60 °. The height of the rhombus, omitted from the top of the obtuse angle, divides the side into two segments. What are the lengths of these segments?
Consider a triangle ABC, this triangle is rectangular (by the condition of the problem). ∠A = 60 °, therefore, by the theorem on the sum of the angles of a triangle, ∠ABС = 180 ° -90 ° -60 ° = 30 °. By the property of a right triangle AC = AB / 2 = 32/2 = 16. Therefore, the second half of the side of the rhombus = 32-16 = 16. That is, in this task, the height drawn to the side of the rhombus divides this side into two equal parts.
Answer: the lengths of both segments are 16
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