Longer Side of Scalene Triangle given Larger Angle and other Sides Calculator

Formula Used:

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

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Larger Angle of Scalene Triangle:

Longer Side of Scalene Triangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

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

The formula calculates the length of the longer side of a scalene triangle when given the medium side, shorter side, and the larger angle. It's derived from the Law of Cosines, which relates the sides and angles of any triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

Medium Side — Length of the second longest side (meters)
Shorter Side — Length of the shortest side (meters)
Larger Angle — The angle opposite the longer side (degrees)
cos — Cosine trigonometric function
sqrt — Square root function

Explanation: This formula applies the Law of Cosines to find the side opposite the given angle when the other two sides are known.

3. Importance of Calculating the Longer Side

Details: Calculating the longer side is essential for complete triangle analysis, construction planning, and various engineering applications where all triangle dimensions need to be determined.

4. Using the Calculator

Tips: Enter the medium side and shorter side lengths in meters, and the larger angle in degrees. All values must be positive, and the angle must be between 0° and 180°.

5. Frequently Asked Questions (FAQ)

Q1: Why use the Law of Cosines instead of the Law of Sines?
A: The Law of Cosines is used when you know two sides and the included angle, while the Law of Sines is used when you know two angles and one side.

Q2: What is a scalene triangle?
A: A scalene triangle is a triangle where all three sides have different lengths and all three angles have different measures.

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

Q4: What if the angle is 90 degrees?
A: When the angle is 90°, cos(90°) = 0, and the formula reduces to the Pythagorean theorem.

Q5: How accurate are the results?
A: The results are mathematically precise based on the input values, with rounding to 6 decimal places for practical use.