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The acute angle between diagonals of a rectangle is the smaller angle formed where the two diagonals intersect. In any rectangle, the diagonals are equal in length and bisect each other, creating two acute angles and two obtuse angles at their intersection point.
The calculator uses the formula:
Where:
Explanation: In a rectangle, the acute and obtuse angles between diagonals are supplementary angles, meaning they add up to π radians (180 degrees).
Details: The diagonals of a rectangle have several important properties: they are equal in length, bisect each other, and create complementary angle pairs where the acute and obtuse angles sum to 180 degrees (π radians).
Tips: Enter the obtuse angle between diagonals in radians. The value must be greater than π/2 (1.5708 radians) and less than π (3.1416 radians) to be valid.
Q1: Why do the acute and obtuse angles sum to π radians?
A: Because the angles formed by intersecting diagonals in a rectangle are supplementary - they lie on a straight line and therefore sum to 180 degrees (π radians).
Q2: What is the typical range for the acute angle?
A: The acute angle between diagonals of a rectangle typically ranges from 0 to π/2 radians (0 to 90 degrees), depending on the rectangle's proportions.
Q3: How does rectangle shape affect these angles?
A: In a square (special rectangle), all angles between diagonals are equal to π/2 radians (90 degrees). As the rectangle becomes more elongated, one angle becomes more acute while the other becomes more obtuse.
Q4: Can I use degrees instead of radians?
A: The calculator requires radians. To convert degrees to radians, multiply by π/180. For example, 90° = π/2 ≈ 1.5708 radians.
Q5: What if I know the rectangle's side lengths instead?
A: If you know the length and width, you can calculate the angles using trigonometric functions: acute angle = 2 × arctan(width/length).