Trapezoid Angle Calculator from Sides

Angle Calculation Formula:

\[ \text{angle} = \arccos\left(\frac{\text{leg}^2 + \text{base}^2 - \text{side}^2}{2 \times \text{leg} \times \text{base}}\right) \]

Angle (degrees):

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1. What is the Trapezoid Angle Calculator?

This calculator determines the angle between the leg and base of a trapezoid when you know the lengths of three sides (leg, base, and opposite side). It uses the inverse cosine function based on the Law of Cosines.

2. How Does the Calculator Work?

The calculator uses the following formula:

\[ \text{angle} = \arccos\left(\frac{\text{leg}^2 + \text{base}^2 - \text{side}^2}{2 \times \text{leg} \times \text{base}}\right) \]

Where:

\( \text{leg} \) — Length of one non-parallel side (m)
\( \text{base} \) — Length of the base side (m)
\( \text{side} \) — Length of the opposite side (m)
The result is in degrees

Explanation: This formula comes from rearranging the Law of Cosines to solve for the angle between two known sides when the third side is known.

3. Importance of Angle Calculation

Details: Knowing trapezoid angles is essential in construction, engineering, and geometry problems. It helps in determining the exact shape and properties of the trapezoid.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The values must satisfy the triangle inequality (sum of any two sides must be greater than the third side).

5. Frequently Asked Questions (FAQ)

Q1: What units should I use?
A: The calculator uses meters, but you can use any consistent unit as long as all three measurements are in the same unit.

Q2: What if I get an error message?
A: This means your side lengths don't satisfy the triangle inequality. Check that the sum of any two sides is greater than the third side.

Q3: Can I use this for any quadrilateral?
A: No, this specifically calculates the angle between two adjacent sides when you know the length of the opposite side in a trapezoid.

Q4: How accurate is the calculation?
A: The calculation is mathematically precise, but practical accuracy depends on the precision of your input measurements.

Q5: Does this work for right trapezoids?
A: Yes, it works for all trapezoids where you know the three required side lengths.