Oblique Triangle Calculator Trigonometry

Law of Cosines:

\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]

Side c:

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1. What is the Law of Cosines?

The Law of Cosines is a formula relating the lengths of the sides of a triangle to the cosine of one of its angles. It generalizes the Pythagorean theorem for oblique (non-right) triangles.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines:

\[ c^2 = a^2 + b^2 - 2ab \cos(C) \]

Where:

\( a \) — Length of side a
\( b \) — Length of side b
\( C \) — Angle between sides a and b (in degrees)
\( c \) — Length of the side opposite angle C

Explanation: The formula calculates the third side of a triangle when you know two sides and the included angle.

3. Importance of the Law of Cosines

Details: This law is essential in trigonometry for solving oblique triangles, navigation, physics, and engineering applications where right triangles aren't present.

4. Using the Calculator

Tips: Enter lengths of sides a and b, and the included angle C in degrees. All values must be positive, and angle must be between 0 and 180 degrees.

5. Frequently Asked Questions (FAQ)

Q1: When should I use the Law of Cosines?
A: Use it when you know two sides and the included angle (SAS) or when you know all three sides (SSS) of a triangle.

Q2: How does this differ from the Law of Sines?
A: The Law of Sines relates sides to opposite angles, while the Law of Cosines relates all three sides to one angle.

Q3: Can this be used for right triangles?
A: Yes, but when angle C is 90°, the formula reduces to the Pythagorean theorem since cos(90°) = 0.

Q4: What units should I use?
A: Any consistent units for length (cm, m, inches, etc.). Angles must be in degrees.

Q5: What if my angle is in radians?
A: Convert radians to degrees first (1 radian ≈ 57.2958 degrees) or modify the code to accept radians.