1. What is the Law of Sines Calculator?

Definition: This calculator solves for unknown sides or angles in non-right triangles using the Law of Sines formula.

Purpose: It helps in trigonometry problems involving oblique triangles where the standard right-angle formulas don't apply.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( A, B \) — Angles opposite sides a, b (degrees)
• \( a, b \) — Sides of the triangle (meters)

Explanation: The ratio of the sine of an angle to the length of its opposite side is constant for all angles in a triangle.

3. Importance of Law of Sines

Details: Essential for solving triangles in navigation, surveying, and physics problems where right angles aren't present.

4. Using the Calculator

Tips: Enter any two angles and one side (ASA case) or two sides and one opposite angle (SSA case). Angles must be in degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the ambiguous case in Law of Sines?
A: When given two sides and a non-included angle (SSA), there may be two possible solutions.

Q2: Can I use this for right triangles?
A: Yes, but right triangles can be solved more simply with Pythagorean theorem.

Q3: What units should I use?
A: Angles must be in degrees. Side units can be any consistent length (meters shown).

Q4: How do I find the third angle?
A: Subtract the two known angles from 180° (triangle angle sum).

Q5: What if I get an error?
A: Check that angles sum to less than 180° and sides are positive numbers.