Area Of Scalene Triangle Given Medium Angle And Adjacent Sides Calculator

Area of Scalene Triangle Formula:

\[ A = \frac{S_{Longer} \times S_{Shorter} \times \sin(\angle_{Medium})}{2} \]

Longer Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Medium Angle of Scalene Triangle:

Area of Scalene Triangle:

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1. What is the Area of Scalene Triangle Formula?

The formula calculates the area of a scalene triangle when you know the lengths of two adjacent sides and the included angle between them. This is particularly useful when you have the longer side, shorter side, and the medium angle of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ A = \frac{S_{Longer} \times S_{Shorter} \times \sin(\angle_{Medium})}{2} \]

Where:

\( A \) — Area of Scalene Triangle (m²)
\( S_{Longer} \) — Longer Side of Scalene Triangle (m)
\( S_{Shorter} \) — Shorter Side of Scalene Triangle (m)
\( \angle_{Medium} \) — Medium Angle of Scalene Triangle (degrees)
\( \sin \) — Sine trigonometric function

Explanation: The formula uses the trigonometric relationship between two sides and their included angle to calculate the area of the triangle.

3. Importance of Area Calculation

Details: Calculating the area of a scalene triangle is essential in various fields including geometry, engineering, architecture, and construction where precise area measurements are required for irregular triangular shapes.

4. Using the Calculator

Tips: Enter the longer side and shorter side in meters, and the medium angle in degrees. All values must be valid (sides > 0, angle between 0-180 degrees).

5. Frequently Asked Questions (FAQ)

Q1: Why use this specific formula for area calculation?
A: This formula is particularly useful when you know two adjacent sides and the included angle, which is a common scenario in practical applications.

Q2: What units should I use for the inputs?
A: The sides should be in meters and the angle in degrees. The calculator will automatically convert degrees to radians for the sine function.

Q3: Can I use this calculator for any triangle?
A: This calculator is specifically designed for scalene triangles where all sides have different lengths and all angles are different.

Q4: What if I have the angle in radians instead of degrees?
A: This calculator expects the angle in degrees. If you have radians, you'll need to convert them to degrees first (radians × 180/π).

Q5: How accurate are the results?
A: The results are accurate to 6 decimal places, which is sufficient for most practical applications in geometry and engineering.