Angle Between Diagonal and Breadth of Rectangle Given Diameter of Circumcircle and Length Calculator

Formula Used:

\[ \text{Angle between Diagonal and Breadth of Rectangle} = \arcsin\left(\frac{\text{Length of Rectangle}}{\text{Diameter of Circumcircle of Rectangle}}\right) \]

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 where the diagonal intersects with 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:

\[ \text{Angle} = \arcsin\left(\frac{\text{Length}}{\text{Diameter}}\right) \]

Where:

Length — Length of the rectangle (longer side)
Diameter — Diameter of the circumcircle that passes through all four vertices of the rectangle

Explanation: The formula uses the inverse sine function to calculate the angle based on the ratio of the rectangle's length to the diameter of its circumcircle.

3. Importance of Angle Calculation

Details: Calculating this angle is important in geometry, engineering, and design applications where precise angular relationships in rectangular shapes are required.

4. Using the Calculator

Tips: Enter the length of the rectangle and the diameter of its circumcircle. Both values must be positive numbers, and the length cannot exceed the diameter.

5. Frequently Asked Questions (FAQ)

Q1: Why is the length divided by the diameter?
A: This ratio represents the sine of the angle between the diagonal and breadth, based on trigonometric relationships in a right triangle formed by the diagonal.

Q2: What is the range of possible values for this angle?
A: The angle ranges from 0° to 90°, with 45° occurring when the rectangle is a square.

Q3: How is the circumcircle diameter related to the rectangle?
A: The diameter of the circumcircle equals the length of the rectangle's diagonal.

Q4: Can this formula be used for any rectangle?
A: Yes, this formula applies to all rectangles regardless of their proportions.

Q5: What if the length is greater than the diameter?
A: This is geometrically impossible since the diagonal (which equals the diameter) is always longer than the length in a rectangle.