Missing Triangle Side Calculator

Law of Cosines:

\[ b = \sqrt{a^2 + c^2 - 2 \cdot a \cdot c \cdot \cos(B)} \]

Missing Side b:

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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 and works for any type of triangle.

2. How Does the Calculator Work?

The calculator uses the Law of Cosines:

\[ b = \sqrt{a^2 + c^2 - 2 \cdot a \cdot c \cdot \cos(B)} \]

Where:

\( a \) — Length of side a (meters)
\( c \) — Length of side c (meters)
\( B \) — Angle between sides a and c (degrees)
\( b \) — Length of the missing side (meters)

Explanation: The formula calculates the length of the third side when two sides and the included angle are known.

3. Importance of Triangle Calculations

Details: These calculations are essential in trigonometry, navigation, engineering, and physics for solving real-world problems involving triangles.

4. Using the Calculator

Tips: Enter the lengths of two sides and the included angle in degrees. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator find angles as well?
A: No, this specific calculator only finds the missing side when two sides and the included angle are known.

Q2: What units should I use?
A: The calculator uses meters for lengths and degrees for angles, but any consistent units will work.

Q3: Does this work for right triangles?
A: Yes, but for right triangles the Pythagorean theorem is simpler (when you know two sides).

Q4: What if I know three sides but no angles?
A: You would need to use the Law of Cosines rearranged to solve for an angle.

Q5: How accurate are the results?
A: Results are accurate to two decimal places, sufficient for most practical applications.