Perimeter Of Scalene Triangle Given Larger Angle And Adjacent Sides Calculator

Formula Used:

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

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

Perimeter of Scalene Triangle:

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1. What is the Perimeter of Scalene Triangle?

The perimeter of a scalene triangle is the total length of its three unequal sides. It represents the complete boundary length of the triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( P \) — Perimeter of Scalene Triangle (m)
\( S_{Medium} \) — Medium side length (m)
\( S_{Shorter} \) — Shorter side length (m)
\( \angle_{Larger} \) — Larger angle (degrees)

Explanation: This 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 various geometric applications, construction projects, and engineering designs where precise measurements of triangular boundaries are required.

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, 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 this specific formula?
A: This formula is particularly useful when you know two sides and the included angle (the larger angle between them) and need to find the perimeter.

Q3: Can this calculator handle different units?
A: The calculator uses meters as the default unit, but you can use any consistent unit of length as long as all side measurements are in the same unit.

Q4: What if I have the third side instead of the angle?
A: If you have all three sides, simply add them together to get the perimeter without needing this formula.

Q5: How accurate are the results?
A: The results are accurate to six decimal places, providing precision for most practical applications.