Angle Between Diagonal And Breadth Of Rectangle Given Breadth And Circumradius Calculator

Formula Used:

\[ \text{Angle between Diagonal and Breadth of Rectangle} = \arccos\left(\frac{\text{Breadth of Rectangle}}{2 \times \text{Circumradius of Rectangle}}\right) \]

Angle between Diagonal and Breadth of Rectangle:

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1. What is the Angle between Diagonal and Breadth of Rectangle?

The angle between the diagonal and breadth of a rectangle is the acute angle formed between the diagonal and the shorter side (breadth) of the rectangle. This angle helps in understanding the geometric properties and proportions of the rectangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Angle} = \arccos\left(\frac{b}{2 \times r_c}\right) \]

Where:

\( b \) — Breadth of the rectangle (m)
\( r_c \) — Circumradius of the rectangle (m)
\( \arccos \) — Inverse cosine function

Explanation: The formula calculates the angle using the trigonometric relationship between the breadth, circumradius, and the diagonal of the rectangle.

3. Importance of Angle Calculation

Details: Calculating the angle between the diagonal and breadth is important in geometry, engineering, and design applications where precise angular measurements are required for structural integrity and aesthetic proportions.

4. Using the Calculator

Tips: Enter the breadth and circumradius of the rectangle in meters. Both values must be positive numbers. The calculator will compute the angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of the angle between diagonal and breadth?
A: The angle ranges from 0° to 90°, depending on the proportions of the rectangle.

Q2: How is circumradius related to rectangle dimensions?
A: The circumradius is half the length of the diagonal of the rectangle.

Q3: Can this calculator be used for squares?
A: Yes, for a square (where length equals breadth), the angle would be 45°.

Q4: What units should I use for inputs?
A: The calculator uses meters, but any consistent unit of length can be used as the calculation is ratio-based.

Q5: Why does the formula use arccos function?
A: The arccos function is used to find the angle whose cosine equals the ratio of breadth to twice the circumradius, based on trigonometric relationships in right triangles.