Medium Side of Scalene Triangle given Medium Angle and other Sides Calculator

Formula Used:

\[ \text{Medium Side of Scalene Triangle} = \sqrt{\text{Longer Side of Scalene Triangle}^2 + \text{Shorter Side of Scalene Triangle}^2 - 2 \times \text{Longer Side of Scalene Triangle} \times \text{Shorter Side of Scalene Triangle} \times \cos(\text{Medium Angle of Scalene Triangle})} \]

Longer Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Medium Angle of Scalene Triangle:

Medium Side of Scalene Triangle:

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1. What is the Medium Side of Scalene Triangle?

The Medium Side of Scalene Triangle is the length of the second longer side out of the three sides. In a scalene triangle, all three sides have different lengths, and the medium side falls between the longest and shortest sides.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ S_{\text{medium}} = \sqrt{S_{\text{longer}}^2 + S_{\text{shorter}}^2 - 2 \times S_{\text{longer}} \times S_{\text{shorter}} \times \cos(\angle_{\text{medium}})} \]

Where:

\( S_{\text{medium}} \) — Medium Side of Scalene Triangle (m)
\( S_{\text{longer}} \) — Longer Side of Scalene Triangle (m)
\( S_{\text{shorter}} \) — Shorter Side of Scalene Triangle (m)
\( \angle_{\text{medium}} \) — Medium Angle of Scalene Triangle (°)

Explanation: This formula uses the Law of Cosines to calculate the medium side when the longer side, shorter side, and the medium angle are known.

3. Importance of Medium Side Calculation

Details: Calculating the medium side is essential for determining the complete dimensions of a scalene triangle, which is crucial in various geometric calculations, construction projects, and engineering applications.

4. Using the Calculator

Tips: Enter the longer side and shorter side in meters, and the medium angle in degrees. All values must be valid (sides > 0, angle between 0-180°).

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 for this calculation?
A: The Law of Cosines is used when we know two sides and the included angle, and need to find the third side.

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 if I know different parameters?
A: Different formulas would be needed if you know other combinations of sides and angles, such as using the Law of Sines.

Q5: How accurate are the results?
A: The results are accurate to 6 decimal places, which is sufficient for most practical applications in geometry and engineering.