Obtuse Angle between Diagonals of Rectangle given Diameter of Circumcircle and Breadth Calculator

Formula Used:

\[ \text{Obtuse Angle between Diagonals of Rectangle} = 2 \times \arccos\left(\frac{\text{Breadth of Rectangle}}{\text{Diameter of Circumcircle of Rectangle}}\right) \] \[ \angle d(\text{Obtuse}) = 2 \times \arccos\left(\frac{b}{D_c}\right) \]

Obtuse Angle between Diagonals of Rectangle:

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1. What is Obtuse Angle between Diagonals of Rectangle?

The obtuse angle between diagonals of a rectangle is the angle formed by the intersection of the two diagonals that measures more than 90 degrees. In any rectangle, the diagonals are equal in length and bisect each other, creating two acute angles and two obtuse angles.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \angle d(\text{Obtuse}) = 2 \times \arccos\left(\frac{b}{D_c}\right) \]

Where:

\( \angle d(\text{Obtuse}) \) — Obtuse angle between diagonals (radians)
\( b \) — Breadth of Rectangle (m)
\( D_c \) — Diameter of Circumcircle of Rectangle (m)

Explanation: The formula calculates the obtuse angle between the diagonals using the inverse cosine function based on the ratio of the rectangle's breadth to the diameter of its circumcircle.

3. Importance of Angle Calculation

Details: Calculating the angle between diagonals is important in geometry, architectural design, and various engineering applications where precise angular measurements are required for rectangular structures.

4. Using the Calculator

Tips: Enter the breadth of the rectangle and the diameter of its circumcircle in meters. Both values must be positive, and the breadth cannot exceed the diameter.

5. Frequently Asked Questions (FAQ)

Q1: Why is there an obtuse angle between diagonals?
A: In a rectangle, the diagonals intersect and create four angles - two acute and two obtuse. The obtuse angles are always greater than 90 degrees.

Q2: What is the relationship between the acute and obtuse angles?
A: The acute and obtuse angles between the diagonals are supplementary, meaning they add up to 180 degrees.

Q3: Can the breadth be greater than the diameter?
A: No, in a rectangle, the breadth cannot exceed the diameter of the circumcircle, as the diameter equals the length of the diagonal.

Q4: What are typical applications of this calculation?
A: This calculation is used in construction, furniture design, CAD modeling, and any field involving rectangular geometry.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise when correct values are input, as it's based on trigonometric principles.