Triangle Sides and Angles Calculator

Triangle Formulas:

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

Side a:

Side b:

Side c:

Angle A:

Angle B:

Angle C:

Calculated Side a:

Calculated Side b:

Calculated Side c:

Calculated Angle A:

Calculated Angle B:

Calculated Angle C:

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1. What is a Triangle Sides and Angles Calculator?

Definition: This calculator determines unknown sides and angles in a triangle using the Law of Sines and Law of Cosines.

Purpose: It helps solve triangles when you know any combination of three elements (sides or angles), with at least one side.

2. How Does the Calculator Work?

The calculator uses two fundamental trigonometric formulas:

\[ \text{Law of Sines: } \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \] \[ \text{Law of Cosines: } c^2 = a^2 + b^2 - 2ab \times \cos C \]

Where:

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

Explanation: The calculator determines missing elements based on the known values using these trigonometric relationships.

3. Importance of Triangle Calculations

Details: Accurate triangle calculations are essential in fields like engineering, architecture, navigation, and physics for solving spatial problems.

4. Using the Calculator

Tips: Enter any three known values (must include at least one side). The calculator will solve for the remaining sides and angles.

5. Frequently Asked Questions (FAQ)

Q1: What's the minimum information needed to solve a triangle?
A: You need at least three elements (sides or angles), with at least one being a side length.

Q2: When should I use Law of Sines vs. Law of Cosines?
A: Use Law of Sines when you know two angles and one side, or two sides and a non-included angle. Use Law of Cosines when you know three sides or two sides and the included angle.

Q3: What if my inputs don't form a valid triangle?
A: The calculator will detect invalid combinations (like angles summing > 180° or sides violating the triangle inequality).

Q4: How precise are the results?
A: Results are accurate to 3 decimal places, sufficient for most practical applications.

Q5: Can I solve right triangles with this?
A: Yes, though right triangles can be solved with simpler Pythagorean theorem and basic trigonometry.