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

Formula Used:

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

Shorter Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

Smaller Angle of Scalene Triangle:

Longer Side of Scalene Triangle:

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

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

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Longer Side — The side opposite to the larger angle (measured in meters)
Shorter Side — The side opposite to the smaller angle (measured in meters)
Larger Angle — The angle opposite to the longer side (measured in degrees)
Smaller Angle — The angle opposite to the shorter side (measured in degrees)

Explanation: The formula applies the Law of Sines to find the relationship between the sides and their opposite angles in a scalene triangle.

3. Importance of Triangle Side Calculation

Details: Calculating triangle sides is fundamental in geometry, trigonometry, and various practical applications including construction, navigation, and engineering design where triangular structures or measurements are involved.

4. Using the Calculator

Tips: Enter the shorter side length in meters, and both angles in degrees. All values must be positive numbers. The larger angle should be greater than the smaller angle for valid triangle geometry.

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 sides and their opposite angles, making it ideal for calculating unknown sides when angles and one side are known.

Q3: Can this formula be used for any triangle?
A: Yes, the Law of Sines applies to all triangles, not just scalene triangles. However, this specific formulation is particularly useful for scalene triangles where all sides are different.

Q4: What if the angles don't add up to 180 degrees?
A: The calculator assumes valid triangle geometry. For a valid triangle, the sum of all three angles must equal 180 degrees.

Q5: How accurate are the results?
A: The results are mathematically precise based on the input values. The calculator uses PHP's built-in trigonometric functions which provide high precision calculations.