Smaller Angle of Scalene Triangle given Longer Side, Shorter Side and Larger Angle Calculator

Formula Used:

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

Shorter Side of Scalene Triangle:

Longer Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

Smaller Angle of Scalene Triangle:

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1. What is the Smaller Angle of Scalene Triangle?

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

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Shorter Side — Length of the shorter side of the triangle (meters)
Longer Side — Length of the longer side of the triangle (meters)
Larger Angle — Measure of the larger angle in the triangle (degrees)

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

3. Importance of Angle Calculation

Details: Calculating angles in scalene triangles is crucial for geometric analysis, construction planning, and various engineering applications where precise angle measurements are required.

4. Using the Calculator

Tips: Enter the shorter side and longer side in meters, and the larger angle in degrees. All values must be valid (sides > 0, angle between 0-180°).

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 arcsin function in this calculation?
A: The arcsin function is used to find the angle whose sine equals the calculated ratio, allowing us to determine the smaller angle from the side relationships.

Q3: What are the typical angle ranges in a scalene triangle?
A: In any triangle, the sum of angles is always 180°. In a scalene triangle, all three angles are different and typically range from just above 0° to just below 180°.

Q4: Can this formula be used for any triangle?
A: This specific formula is derived from the Law of Sines and works for any triangle where the longer side, shorter side, and larger angle are known.

Q5: What if the calculated angle exceeds 90 degrees?
A: The formula will correctly calculate the smaller angle, which by definition in this context should be less than the larger angle provided.