Perimeter of Scalene Triangle given Smaller Angle and Adjacent Sides Calculator

Perimeter of Scalene Triangle Formula:

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

Longer Side of Scalene Triangle:

Medium Side of Scalene Triangle:

Smaller 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 around the triangle, calculated by summing the lengths of all three sides. In a scalene triangle, all three sides have different lengths and all three angles are different.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( P \) — Perimeter of Scalene Triangle (m)
\( S_{Longer} \) — Longer side of Scalene Triangle (m)
\( S_{Medium} \) — Medium side of Scalene Triangle (m)
\( \angle_{Smaller} \) — Smaller angle of Scalene Triangle (radians)

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

3. Importance of Perimeter Calculation

Details: Calculating the perimeter of a scalene triangle is essential in various geometric applications, construction projects, land surveying, and many engineering fields where precise measurements are required.

4. Using the Calculator

Tips: Enter the longer side and medium side in meters, and the smaller angle in degrees. All values must be valid (sides > 0, angle between 0-90°).

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 calculation?
A: The Law of Cosines allows us to find the third side when we know two sides and the included angle, which is essential for calculating the perimeter.

Q3: Can this calculator be used for other types of triangles?
A: While the formula works for any triangle, this calculator is specifically designed for scalene triangles where all sides are different.

Q4: 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 the angle to radians for the trigonometric calculation.

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