Length of Rectangle given Circumradius and Obtuse Angle between Diagonals Calculator

Formula Used:

\[ l = 2 \times r_c \times \sin(\frac{\angle_{d(obtuse)}}{2}) \]

Length of Rectangle:

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1. What is the Length of Rectangle given Circumradius and Obtuse Angle between Diagonals?

This calculation determines the length of a rectangle using its circumradius (radius of the circumscribed circle) and the obtuse angle between its diagonals. This geometric relationship is derived from the properties of rectangles and trigonometric functions.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ l = 2 \times r_c \times \sin(\frac{\angle_{d(obtuse)}}{2}) \]

Where:

\( l \) — Length of Rectangle (m)
\( r_c \) — Circumradius of Rectangle (m)
\( \angle_{d(obtuse)} \) — Obtuse Angle between Diagonals of Rectangle (°)

Explanation: The formula utilizes the sine trigonometric function to relate the rectangle's length to its circumradius and the angle between its diagonals.

3. Importance of Length Calculation

Details: Calculating the length of a rectangle using circumradius and diagonal angles is important in geometry, engineering design, and architectural planning where these specific measurements might be known or easier to measure.

4. Using the Calculator

Tips: Enter the circumradius in meters and the obtuse angle between diagonals in degrees (must be between 90° and 180°). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the circumradius of a rectangle?
A: The circumradius is the radius of the circle that passes through all four vertices of the rectangle, equal to half the length of the diagonal.

Q2: Why is the angle between diagonals important?
A: The diagonals of a rectangle create four angles - two acute and two obtuse. The obtuse angle helps determine the rectangle's proportions.

Q3: Can this formula be used for any rectangle?
A: Yes, this formula applies to all rectangles as it's derived from fundamental geometric properties of rectangles.

Q4: What if I know the acute angle instead?
A: The acute angle between diagonals is supplementary to the obtuse angle (they sum to 180°), so you can calculate one from the other.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact, assuming precise input values. Real-world accuracy depends on the precision of your measurements.