Triangle Calculator Angles Sides

Triangle Equations:

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

Side a:

units

Side b:

units

Side c:

units

Angle A:

degrees

Angle B:

degrees

Angle C:

degrees

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 the Law of Sines and Cosines?

The Law of Sines and Cosines are trigonometric relationships that allow calculation of unknown sides and angles in any triangle. The Law of Sines relates sides to their opposite angles, while the Law of Cosines generalizes the Pythagorean theorem.

2. How Does the Calculator Work?

The calculator uses these fundamental equations:

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

Where:

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

Explanation: The calculator can solve for any unknown sides or angles when given sufficient information (SSS, SAS, ASA, AAS cases).

3. Importance of Triangle Calculations

Details: These calculations are fundamental in geometry, physics, engineering, navigation, and computer graphics for determining distances and angles when complete information isn't available.

4. Using the Calculator

Tips: Enter any three values (sides or angles) to calculate the remaining values. Ensure the values can form a valid triangle (sum of angles = 180°, sides satisfy triangle inequality).

5. Frequently Asked Questions (FAQ)

Q1: What cases can this calculator solve?
A: It solves SSS (three sides), SAS (two sides and included angle), ASA (two angles and included side), and AAS (two angles and non-included side) cases.

Q2: What units should I use?
A: Any consistent length units for sides (cm, m, inches, etc.). Angles can be in degrees or radians (this calculator uses degrees).

Q3: What if I get an error?
A: Check that your inputs can form a valid triangle. The sum of angles must be 180°, and the sum of any two sides must exceed the third.

Q4: Can this solve right triangles?
A: Yes, but right triangles can also be solved with simpler Pythagorean theorem and basic trig functions.

Q5: How accurate are the results?
A: Results are accurate to two decimal places. For critical applications, verify with alternative methods.