Perimeter of Scalene Triangle given Medium Angle and Adjacent Sides Calculator

Perimeter of Scalene Triangle Formula:

\[ P = S_{Longer} + S_{Shorter} + \sqrt{S_{Longer}^2 + S_{Shorter}^2 - 2 \times S_{Longer} \times S_{Shorter} \times \cos(\angle_{Medium})} \]

Longer Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Medium Angle of Scalene Triangle:

Perimeter of Scalene Triangle:

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1. What is the Perimeter of Scalene Triangle Formula?

The perimeter of a scalene triangle is calculated using the formula that considers the two known sides and the included medium angle. This formula uses the Law of Cosines to determine the third side and then sums all three sides to find the total perimeter.

2. How Does the Calculator Work?

The calculator uses the perimeter formula:

\[ P = S_{Longer} + S_{Shorter} + \sqrt{S_{Longer}^2 + S_{Shorter}^2 - 2 \times S_{Longer} \times S_{Shorter} \times \cos(\angle_{Medium})} \]

Where:

\( P \) — Perimeter of Scalene Triangle (m)
\( S_{Longer} \) — Longer side of the triangle (m)
\( S_{Shorter} \) — Shorter side of the triangle (m)
\( \angle_{Medium} \) — Medium angle between the two sides (degrees)

Explanation: The formula calculates the third side using the Law of Cosines and then sums all three sides to find the total perimeter.

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a scalene triangle is essential in geometry, construction, and various engineering applications where precise measurements of triangular shapes are required.

4. Using the Calculator

Tips: Enter the longer side and shorter side in meters, and the medium angle in degrees. All values must be positive, with the angle between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

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

Q2: Why use the Law of Cosines in this formula?
A: The Law of Cosines is used to find the third side when two sides and the included angle are known, which is essential for calculating the perimeter.

Q3: Can this formula be used for any triangle?
A: This specific formula is designed for scalene triangles where the medium angle is between the longer and shorter sides.

Q4: What units should be used for inputs?
A: Sides should be in meters and angle in degrees. The calculator will output perimeter in meters.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values, with results rounded to 6 decimal places for clarity.