Medium Side of Scalene Triangle given Medium Angle, Larger Angle and Longer Side Calculator

Formula Used:

\[ S_{Medium} = S_{Longer} \times \frac{\sin(\angle_{Medium})}{\sin(\angle_{Larger})} \]

Longer Side of Scalene Triangle:

Medium Angle of Scalene Triangle:

rad

Larger Angle of Scalene Triangle:

rad

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, where all sides have different lengths and all angles are different.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

\[ S_{Medium} = S_{Longer} \times \frac{\sin(\angle_{Medium})}{\sin(\angle_{Larger})} \]

Where:

\( S_{Medium} \) — Medium Side of Scalene Triangle (m)
\( S_{Longer} \) — Longer Side of Scalene Triangle (m)
\( \angle_{Medium} \) — Medium Angle of Scalene Triangle (rad)
\( \angle_{Larger} \) — Larger Angle of Scalene Triangle (rad)

Explanation: This formula uses the Law of Sines to calculate the medium side when the longer side and the angles opposite to both sides are known.

3. Importance of Medium Side Calculation

Details: Calculating the medium side is essential for solving scalene triangles, determining triangle properties, and solving geometric problems in various fields including engineering, architecture, and physics.

4. Using the Calculator

Tips: Enter the longer side length in meters, medium angle in radians, and larger angle in radians. All values must be positive and angles should be within valid range (0 to π radians).

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 radians instead of degrees?
A: The trigonometric functions in the formula work with radians. If you have angles in degrees, convert them to radians first (radians = degrees × π/180).

Q3: What if the angles don't add up to π radians?
A: The sum of angles in any triangle must equal π radians (180°). If your angles don't sum to π, they don't form a valid triangle.

Q4: Can this formula be used for any triangle?
A: This formula specifically applies to scalene triangles where all sides and angles are different, but it works for any triangle as long as the appropriate angles and sides are known.

Q5: What are typical applications of this calculation?
A: This calculation is used in surveying, navigation, structural design, and any field requiring precise geometric calculations with triangles.