Median On Longer Side Of Scalene Triangle Given Larger Angle And Adjacent Sides Calculator

Formula Used:

\[ Median_{Longer} = \frac{\sqrt{S_{Medium}^2 + S_{Shorter}^2 + 2 \times S_{Medium} \times S_{Shorter} \times \cos(\angle_{Larger})}}{2} \]

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

Median on Longer Side of Scalene Triangle:

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1. What is the Median on Longer Side of Scalene Triangle?

The median on the longer side of a scalene triangle is a line segment joining the midpoint of the longer side to its opposite vertex. It divides the triangle into two smaller triangles of equal area.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ Median_{Longer} = \frac{\sqrt{S_{Medium}^2 + S_{Shorter}^2 + 2 \times S_{Medium} \times S_{Shorter} \times \cos(\angle_{Larger})}}{2} \]

Where:

\( S_{Medium} \) — Medium side of the scalene triangle (m)
\( S_{Shorter} \) — Shorter side of the scalene triangle (m)
\( \angle_{Larger} \) — Larger angle of the scalene triangle (degrees)

Explanation: This formula calculates the median length using the adjacent sides and the included larger angle through trigonometric relationships.

3. Importance of Median Calculation

Details: Medians are important geometric elements that help in understanding triangle properties, calculating centroids, and solving various geometric problems involving triangle division and area calculations.

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°.

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: How is the median different from the altitude?
A: The median connects a vertex to the midpoint of the opposite side, while the altitude is perpendicular from a vertex to the opposite side.

Q3: Can this formula be used for any triangle?
A: This specific formula is designed for calculating the median on the longer side of a scalene triangle when the adjacent sides and included larger angle are known.

Q4: What units should I use for the inputs?
A: The calculator accepts side lengths in meters and angles in degrees. The result will be in meters.

Q5: How accurate is the calculation?
A: The calculation provides results with 6 decimal places precision, making it suitable for most geometric applications.