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

Formula Used:

\[ \text{Medium Angle} = \arcsin\left(\frac{\text{Medium Side}}{\text{Longer Side}} \times \sin(\text{Larger Angle})\right) \]

Medium Side of Scalene Triangle:

Longer Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

rad

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 have different measures.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Medium Angle} = \arcsin\left(\frac{\text{Medium Side}}{\text{Longer Side}} \times \sin(\text{Larger Angle})\right) \]

Where:

Medium Side - The length of the second longer side out of the three sides (in meters)
Longer Side - The length of the longer side out of the three sides (in meters)
Larger Angle - The measure of wideness of sides which join to form the corner opposite to the longer side (in radians)

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

3. Importance of Medium Angle Calculation

Details: Calculating the medium angle is essential for solving scalene triangles, determining triangle properties, and solving geometric problems involving triangles with unequal sides and angles.

4. Using the Calculator

Tips: Enter the medium side and longer side in meters, and the larger angle in radians. All values must be positive numbers. The calculator will provide the result in both radians and 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 use radians instead of degrees?
A: Radians are the standard unit for angle measurement in mathematical calculations, particularly in trigonometry and calculus.

Q3: Can this formula be used for any triangle?
A: This specific formula applies to scalene triangles where the longer side, medium side, and larger angle are known.

Q4: What if the calculated angle exceeds 90 degrees?
A: The calculator will correctly calculate angles up to 180 degrees, but in a valid triangle, all angles must be less than 180 degrees and sum to exactly 180 degrees.

Q5: How accurate is the calculation?
A: The calculation is mathematically precise based on the input values, with results rounded to 6 decimal places for radians and 2 decimal places for degrees.