1. What is the Law of Sines?

The Law of Sines is a trigonometric equation relating 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:

Where:

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

Explanation: The Law of Sines allows calculation of unknown sides or angles when you know:

• Two angles and any side (AAS or ASA)
• Two sides and an angle opposite one of them (SSA, the ambiguous case)

3. Solving Oblique Triangles

Details: The calculator handles two main cases:

1. AAS/ASA: When two angles and any side are known, the third angle is found by subtracting from 180°, then other sides are calculated.
2. SSA (Ambiguous Case): When two sides and a non-included angle are known, there may be 0, 1, or 2 possible solutions.

4. Using the Calculator

Tips: Enter at least three known values (including at least one side). Angles must be in degrees (0-180°). For SSA cases, the calculator will show all possible solutions.

5. Frequently Asked Questions (FAQ)

Q1: Why might there be two solutions for SSA case?
A: When given two sides and a non-included angle (SSA), the information may describe two different triangles, one triangle, or sometimes no triangle.

Q2: What's the ambiguous case?
A: The SSA condition is called "ambiguous" because it can result in zero, one, or two solutions depending on the given values.

Q3: When does SSA have no solution?
A: When the given side opposite the given angle is too short to reach the other given side, forming no triangle.

Q4: Can I use this for right triangles?
A: Yes, but right triangles have simpler trigonometric relationships (Pythagorean theorem, basic trig ratios).

Q5: What units should I use?
A: Any consistent units for sides (cm, inches, etc.). Angles must be in degrees (0-180°).