Triangle Angle Calculator 2 Sides 1 Angle

Law of Sines Formula:

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

Angle B (degrees):

Angle C (degrees):

Side c (meters):

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1. What is the Triangle Angle Calculator (2 Sides 1 Angle)?

Definition: This calculator determines the remaining angles and side of a triangle when you know two sides and one non-included angle using the Law of Sines.

Purpose: It helps in solving triangles for geometry, trigonometry, surveying, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the Law of Sines formula:

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

Where:

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

Explanation: Given two sides and one angle, the calculator first finds the second angle using the Law of Sines, then the third angle by the triangle angle sum (180°), and finally the remaining side using the Law of Sines again.

3. Important Notes

Ambiguous Case: When given two sides and a non-included angle (SSA), there may be two possible solutions, one solution, or no solution. The calculator will provide one valid solution when possible.

Limitations: The angle must be between 0° and 180°, and sides must be positive values. The sum of given angle and calculated angle must be less than 180°.

4. Using the Calculator

Tips: Enter the lengths of two sides in meters and the measure of one angle in degrees (must be opposite one of the given sides). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is the ambiguous case in triangle solutions?
A: When given two sides and a non-included angle (SSA), there might be two different possible triangles, one triangle, or no valid triangle.

Q2: How does the calculator handle the ambiguous case?
A: It provides one valid solution when possible. For cases with two solutions, it gives the acute angle solution.

Q3: What if I get "NaN" as a result?
A: This means no valid triangle exists with the given measurements (the values violate triangle properties).

Q4: Can I use this for right triangles?
A: Yes, but right triangles can be solved more simply using Pythagorean theorem and basic trig ratios.

Q5: What units does this calculator use?
A: Sides are in meters and angles are in degrees. You can use any consistent units for sides as long as you're consistent.