Angles from sides using Cosines, Scalene angle

Scalene Triangle Angle Calculator

Angle Calculation Formulas:

\[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \] \[ \cos B = \frac{a^2 + c^2 - b^2}{2ac} \] \[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \]

Angle A:

Angle B:

Angle C:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is a Scalene Triangle Angle Calculator?

Definition: This calculator computes all three angles of a scalene triangle when you know the lengths of all three sides.

Purpose: It helps in geometry, construction, engineering, and design projects where precise angle measurements are needed.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines formulas:

\[ \cos A = \frac{b^2 + c^2 - a^2}{2bc} \] \[ \cos B = \frac{a^2 + c^2 - b^2}{2ac} \] \[ \cos C = \frac{a^2 + b^2 - c^2}{2ab} \]

Where:

\( a, b, c \) — Lengths of the sides (meters)
\( A, B, C \) — Angles opposite to sides a, b, c respectively (degrees)

Explanation: The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles.

3. Importance of Angle Calculation

Details: Accurate angle calculation is crucial for structural integrity in construction, proper fitting in manufacturing, and correct measurements in surveying.

4. Using the Calculator

Tips: Enter all three side lengths in meters. The sum of any two sides must be greater than the third side for a valid triangle.

5. Frequently Asked Questions (FAQ)

Q1: What is a scalene triangle?
A: A scalene triangle has all sides of different lengths and all angles of different measures.

Q2: Does this work for right triangles?
A: Yes, it works for all triangle types, including right, acute, and obtuse triangles.

Q3: What units are used?
A: Sides are in meters, angles are in degrees.

Q4: Why do I get an error message?
A: The sides must satisfy the triangle inequality theorem (sum of any two sides > third side).

Q5: How precise are the results?
A: Results are accurate to two decimal places for angles.