Solve the Oblique Triangle Calculator

Law of Sines:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

Side a:

units

Angle A (degrees):

Side b:

units

Angle B (degrees):

Side c:

units

Angle C (degrees):

Results:

Side a: units

Angle A: °

Side b: units

Angle B: °

Side c: units

Angle C: °

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1. What is the Law of Sines?

The Law of Sines is a fundamental relationship in trigonometry that relates the lengths of sides of a triangle to the sines of its opposite angles. For any triangle (not just right triangles), the ratio of the length of a side to the sine of its opposite angle is constant.

2. How Does the Calculator Work?

The calculator uses the Law of Sines:

\[ \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} \]

Where:

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

Explanation: The calculator can solve for missing sides or angles when given any combination of three elements (sides or angles) of a triangle, as long as at least one side is provided.

3. Types of Triangle Problems Solved

Details: The calculator can handle several cases:

ASA (Angle-Side-Angle): Two angles and the included side
AAS (Angle-Angle-Side): Two angles and a non-included side
SAS (Side-Angle-Side): Two sides and the included angle
SSA (Side-Side-Angle): Two sides and a non-included angle
SSS (Side-Side-Side): Three sides (uses Law of Cosines)

4. Using the Calculator

Tips: Enter any three known values (at least one side) and the calculator will solve for the remaining elements. Angles should be in degrees (0-180°). Side lengths must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if I get an error message?
A: The error might mean the given values don't form a valid triangle (sum of angles > 180°, or sides don't satisfy triangle inequality).

Q2: What about the ambiguous case (SSA)?
A: The SSA case can sometimes have two solutions. The calculator will provide one valid solution.

Q3: Can I use this for right triangles?
A: Yes, but right triangles can be solved more simply with Pythagorean theorem and basic trig functions.

Q4: How precise are the results?
A: Results are rounded to 2 decimal places. For exact values, symbolic computation would be needed.

Q5: What units should I use?
A: Any consistent units for length (cm, m, inches, etc.). Angles must be in degrees.