Obtuse Angle of Right Kite Calculator

Formula Used:

\[ \text{Obtuse Angle} = 2 \times \arccos\left(\frac{S_{\text{Short}}^2 + d_{\text{Symmetry}}^2 - S_{\text{Long}}^2}{2 \times S_{\text{Short}} \times d_{\text{Symmetry}}}\right) \]

Short Side of Right Kite (SShort):

Symmetry Diagonal of Right Kite (dSymmetry):

Long Side of Right Kite (SLong):

Obtuse Angle of Right Kite:

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1. What is the Obtuse Angle of Right Kite?

The Obtuse Angle of Right Kite is the angle made by the pair of short sides of the Right Kite. A Right Kite is a kite that can be inscribed in a circle with all vertices on the circle, and it contains one right angle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Obtuse Angle} = 2 \times \arccos\left(\frac{S_{\text{Short}}^2 + d_{\text{Symmetry}}^2 - S_{\text{Long}}^2}{2 \times S_{\text{Short}} \times d_{\text{Symmetry}}}\right) \]

Where:

\( S_{\text{Short}} \) — Short Side of Right Kite (m)
\( d_{\text{Symmetry}} \) — Symmetry Diagonal of Right Kite (m)
\( S_{\text{Long}} \) — Long Side of Right Kite (m)

Explanation: This formula calculates the obtuse angle using the Law of Cosines applied to the triangle formed by the sides and diagonal of the right kite.

3. Importance of Obtuse Angle Calculation

Details: Calculating the obtuse angle is important for understanding the geometric properties of right kites, which have applications in various fields including architecture, engineering, and design where specific angular relationships are required.

4. Using the Calculator

Tips: Enter all three values in meters. Ensure that the values are positive and form a valid geometric configuration. The calculator will return the obtuse angle in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What is a Right Kite?
A: A Right Kite is a kite that can be inscribed in a circle and contains one right angle. It has two pairs of adjacent sides that are equal in length.

Q2: Why is the obtuse angle important in a right kite?
A: The obtuse angle, along with the right angle, defines the shape and symmetry properties of the right kite, which is crucial in various geometric applications.

Q3: What are the typical values for the obtuse angle?
A: In a right kite, the obtuse angle is always greater than 90° and less than 180°, typically ranging between 90° and 180° depending on the side lengths.

Q4: Can this formula be used for any kite?
A: This specific formula is designed for right kites that have the properties described. For other types of kites, different geometric relationships and formulas may apply.

Q5: What if I get an error message?
A: An error message indicates that the input values do not form a valid geometric configuration for a right kite. Please check your measurements and ensure they satisfy the triangle inequality and other geometric constraints.