Area Of Scalene Triangle Given Larger Angle And Adjacent Sides Calculator

Formula Used:

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

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Larger 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 medium side, shorter side, and the larger angle between them. This method uses trigonometric functions to determine the area without needing the height of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( A \) — Area of Scalene Triangle (m²)
\( S_{Medium} \) — Medium side length (m)
\( S_{Shorter} \) — Shorter side length (m)
\( \angle_{Larger} \) — Larger angle between sides (degrees)

Explanation: The formula uses the sine trigonometric function to calculate the area based on two sides and the included angle.

3. Importance of Area Calculation

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

4. Using the Calculator

Tips: Enter the medium side and shorter side lengths in meters, and the larger angle in degrees. All values must be positive numbers, with the angle between 0 and 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 sides and the included angle, which is common in many practical applications.

Q2: What units should I use for the inputs?
A: Side lengths should be in meters and the angle in degrees. The calculator will automatically handle the conversion to radians for trigonometric calculations.

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

Q4: What if I have the longer side instead of the medium side?
A: This formula requires the medium and shorter sides adjacent to the larger angle. If you have different measurements, you may need to use a different area formula.

Q5: How accurate are the results?
A: The results are accurate to 6 decimal places, providing precise area calculations for most practical applications.