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Scalene Triangle Calculator 2 Sides 1 Angle

Third Side Formula (SAS):

\[ c = \sqrt{a^2 + b^2 - 2ab \cos(C)} \]

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meters
degrees
meters

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1. What is a Scalene Triangle Calculator (2 Sides + 1 Angle)?

Definition: This calculator determines the third side of a scalene triangle when you know two sides and the included angle (SAS).

Purpose: It helps in solving triangular measurements for construction, engineering, and geometry problems.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formula:

\[ c = \sqrt{a^2 + b^2 - 2ab \cos(C)} \]

Where:

Explanation: The formula calculates the missing side by accounting for both the side lengths and the angle between them.

3. Importance of SAS Triangle Calculation

Details: SAS calculations are fundamental in trigonometry and essential for accurate measurements in construction, navigation, and design.

4. Using the Calculator

Tips: Enter the two known side lengths in meters and the included angle in degrees (must be between 0° and 180°).

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A triangle with all sides of different lengths and all angles of different measures.

Q2: Why does the angle need to be between sides a and b?
A: The Law of Cosines specifically requires the angle between the two known sides for accurate calculation.

Q3: What if my angle is exactly 90 degrees?
A: The formula reduces to the Pythagorean theorem (c² = a² + b²) when C = 90°.

Q4: Can I use this for non-scalene triangles?
A: Yes, the formula works for any triangle when you have SAS information.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise when inputs are accurate. Results are shown to 3 decimal places.

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