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. It works for any triangle, not just right-angled ones.

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 ratio of the length of a side to the sine of its opposite angle is constant for all three sides and angles in a triangle.

3. Importance of Triangle Solving

Details: Solving triangles is fundamental in trigonometry, navigation, surveying, and many engineering applications. It allows determination of unknown sides or angles when sufficient information is known.

4. Using the Calculator

Tips: Enter any three known values (sides or angles) to calculate the unknowns. You must provide either:

• Two angles and one side (AAS or ASA cases)
• Two sides and an angle opposite one of them (SSA case)
• Three sides (SSS case)

5. Frequently Asked Questions (FAQ)

Q1: What is the ambiguous case in triangle solving?
A: The SSA case can sometimes have two solutions when the given angle is acute and the opposite side is shorter than the adjacent side.

Q2: Can this calculator handle right triangles?
A: Yes, though right triangles can also be solved using simpler Pythagorean theorem and basic trigonometric ratios.

Q3: What units should I use for angles?
A: The calculator expects angles in degrees. For radians, you would need to convert them first.

Q4: What if my triangle doesn't satisfy the triangle inequality?
A: The calculator should detect invalid inputs where the sum of angles exceeds 180° or sides don't satisfy a + b > c, etc.

Q5: Can this solve for area as well?
A: Once all sides and angles are known, area can be calculated using the formula: Area = ½ab sin C.