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

Formula Used:

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

Longer Side of Scalene Triangle:

Smaller Angle of Scalene Triangle:

Larger Angle of Scalene Triangle:

Shorter Side of Scalene Triangle:

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1. What is the Shorter Side of Scalene Triangle Formula?

The formula calculates the shorter side of a scalene triangle using the longer side and the angles opposite to these sides. It's derived from the Law of Sines, which states that the ratio of a side length to the sine of its opposite angle is constant for all three sides of a triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Longer Side - The length of the longest side of the scalene triangle (meters)
Smaller Angle - The angle opposite the shorter side (degrees)
Larger Angle - The angle opposite the longer side (degrees)

Explanation: The formula applies the Law of Sines to relate the sides and their opposite angles in any triangle.

3. Importance of Triangle Side Calculation

Details: Calculating unknown sides of triangles is fundamental in geometry, trigonometry, and various practical applications including construction, navigation, and engineering design.

4. Using the Calculator

Tips: Enter the longer side length in meters, the smaller angle in degrees, and the larger angle in degrees. Ensure the smaller angle is less than the larger angle, and all values are positive.

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 sine function in this calculation?
A: The sine function relates angles to side ratios in triangles through the Law of Sines, making it essential for solving triangle problems.

Q3: Can this formula be used for any triangle?
A: Yes, the Law of Sines applies to all triangles, not just scalene triangles.

Q4: What if I have the medium side instead of the longer side?
A: The formula specifically requires the longer side and its opposite angle. For other combinations, different arrangements of the Law of Sines would be needed.

Q5: How accurate is this calculation?
A: The calculation is mathematically exact when using precise angle measurements and follows the exact relationships defined by the Law of Sines.