Smaller Angle of Scalene Triangle Calculator

Formula Used:

\[ \angle Smaller = \arccos\left(\frac{S_{Longer}^2 + S_{Medium}^2 - S_{Shorter}^2}{2 \times S_{Longer} \times S_{Medium}}\right) \]

Longer Side of Scalene Triangle:

Medium Side of Scalene Triangle:

Shorter Side of Scalene Triangle:

Smaller Angle of Scalene Triangle:

Unit Converter ▲

Unit Converter ▼

From:	To:

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 derived from the Law of Cosines:

\[ \angle Smaller = \arccos\left(\frac{S_{Longer}^2 + S_{Medium}^2 - S_{Shorter}^2}{2 \times S_{Longer} \times S_{Medium}}\right) \]

Where:

\( S_{Longer} \) — Longer side of the scalene triangle (m)
\( S_{Medium} \) — Medium side of the scalene triangle (m)
\( S_{Shorter} \) — Shorter side of the scalene triangle (m)

Explanation: This formula calculates the angle opposite the shorter side using the lengths of all three sides of the triangle.

3. Importance of Angle Calculation

Details: Calculating angles in scalene triangles is essential for various geometric applications, construction projects, engineering designs, and trigonometric calculations.

4. Using the Calculator

Tips: Enter the lengths of all three sides in meters. All values must be positive numbers that satisfy the triangle inequality theorem.

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 Cosines for this calculation?
A: The Law of Cosines is used when you know all three sides of a triangle and need to find an angle, making it perfect for this calculation.

Q3: What are the valid ranges for side lengths?
A: Side lengths must be positive numbers and must satisfy the triangle inequality theorem (sum of any two sides > third side).

Q4: Can this calculator handle decimal inputs?
A: Yes, the calculator accepts decimal values for more precise calculations.

Q5: What units are used in this calculation?
A: The calculator uses meters for side lengths and degrees for the angle measurement, but the formula works with any consistent unit system.