Larger Angle of Scalene Triangle Calculator

Formula Used:

\[ \text{Larger Angle} = \cos^{-1}\left(\frac{\text{Medium Side}^2 + \text{Shorter Side}^2 - \text{Longer Side}^2}{2 \times \text{Medium Side} \times \text{Shorter Side}}\right) \]

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Longer Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

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1. What is the Larger Angle of Scalene Triangle?

The Larger Angle of a Scalene Triangle is the angle opposite to the longest side of the triangle. In a scalene triangle, all three sides have different lengths, and consequently, all three angles have different measures.

2. How Does the Calculator Work?

The calculator uses the cosine rule formula:

\[ \text{Larger Angle} = \cos^{-1}\left(\frac{\text{Medium Side}^2 + \text{Shorter Side}^2 - \text{Longer Side}^2}{2 \times \text{Medium Side} \times \text{Shorter Side}}\right) \]

Where:

Medium Side - The second longest side of the triangle
Shorter Side - The shortest side of the triangle
Longer Side - The longest side of the triangle (opposite to the larger angle)

Explanation: The formula is derived from the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Angle Calculation

Details: Calculating the larger angle is crucial for understanding triangle properties, solving geometric problems, and applications in various fields such as engineering, architecture, and physics.

4. Using the Calculator

Tips: Enter all three side lengths in meters. Ensure that the side lengths satisfy the triangle inequality theorem (sum of any two sides must be greater than the third side).

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 cosine rule instead of sine rule?
A: The cosine rule is used when we know all three sides of a triangle and want to find an angle, while the sine rule is typically used when we know two angles and one side or two sides and a non-included angle.

Q3: What are the units for the angle result?
A: The angle is calculated in degrees (°).

Q4: What if the input values don't form a valid triangle?
A: The calculator requires that the sum of any two sides must be greater than the third side. If this condition is not met, the inputs do not form a valid triangle.

Q5: Can this calculator be used for other types of triangles?
A: Yes, the cosine rule applies to all types of triangles, including equilateral and isosceles triangles.