Median on Shorter Side of Scalene Triangle given Smaller Angle and Adjacent Sides Calculator

Formula Used:

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

Longer Side of Scalene Triangle:

Medium Side of Scalene Triangle:

Smaller Angle of Scalene Triangle:

Median on Shorter Side of Scalene Triangle:

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1. What is Median on Shorter Side of Scalene Triangle?

The Median on Shorter Side of Scalene Triangle is a line segment joining the midpoint of the shorter side to its opposite vertex. In a scalene triangle, all three sides have different lengths, and this median helps in understanding the triangle's geometric properties.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

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

Explanation: This formula calculates the median length on the shorter side using the adjacent sides (longer and medium) and the included smaller angle through trigonometric relationships.

3. Importance of Median Calculation

Details: Medians in triangles are important geometric elements that help in determining the centroid, which is the center of mass of the triangle. They also play a role in various geometric proofs and constructions.

4. Using the Calculator

Tips: Enter the longer side and medium side in meters, and the smaller angle in degrees. All values must be positive, with the angle between 0-180 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 is the cosine function used in this formula?
A: The cosine function relates the sides and angles of a triangle through the Law of Cosines, which is fundamental in solving triangles when two sides and the included angle are known.

Q3: Can this formula be used for other triangle types?
A: While derived for scalene triangles, this formula works for any triangle where the given sides and angle correspond to the described configuration.

Q4: What units should be used for input?
A: Sides should be in meters and angle in degrees. The calculator will convert degrees to radians internally for trigonometric calculations.

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