Medium Angle of Scalene Triangle given Shorter Side, Medium Side and Smaller Angle Calculator

Formula Used:

\[ \text{Medium Angle of Scalene Triangle} = \sin^{-1}\left(\frac{\text{Medium Side of Scalene Triangle}}{\text{Shorter Side of Scalene Triangle}} \times \sin(\text{Smaller Angle of Scalene Triangle})\right) \]

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Smaller Angle of Scalene Triangle:

Medium Angle of Scalene Triangle:

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1. What is the Medium Angle of Scalene Triangle?

The Medium Angle of Scalene Triangle is the measure of the wideness of sides that join to form the corner opposite to the medium side of the Scalene Triangle. In a scalene triangle, all three angles are different, and the medium angle is the second largest angle.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Medium Angle} = \sin^{-1}\left(\frac{\text{Medium Side}}{\text{Shorter Side}} \times \sin(\text{Smaller Angle})\right) \]

Where:

Medium Side - The length of the second longer side out of the three sides (meters)
Shorter Side - The length of the shorter side out of the three sides (meters)
Smaller Angle - The measure of the wideness of sides that join to form the corner opposite the shorter side (degrees)

Explanation: This formula uses the Law of Sines to calculate the medium angle based on the given side lengths and the smaller angle.

3. Importance of Medium Angle Calculation

Details: Calculating the medium angle is crucial for understanding the geometric properties of scalene triangles, solving triangle problems, and applications in various fields including engineering, architecture, and physics.

4. Using the Calculator

Tips: Enter the medium side and shorter side in meters, and the smaller angle in degrees. All values must be positive, with the smaller 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: Why use the Law of Sines for this calculation?
A: The Law of Sines provides a direct relationship between side lengths and their opposite angles, making it ideal for finding unknown angles when sides and other angles are known.

Q3: What are the typical ranges for medium angles?
A: In a scalene triangle, the medium angle is always between the smallest and largest angles, typically ranging from about 30° to 120°.

Q4: Can this formula be used for any triangle?
A: This specific formula is designed for scalene triangles where all sides and angles are different. For isosceles or equilateral triangles, simplified formulas exist.

Q5: What if the calculated angle exceeds 90 degrees?
A: The calculator properly handles obtuse angles (greater than 90°) as the arcsine function returns values in the appropriate range for triangle angles.