1. What is the Isosceles Triangle Angle Formula?

The isosceles triangle angle formula calculates the vertex angle when you know the lengths of the two equal sides and the base. This is derived from the Law of Cosines applied to an isosceles triangle.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( a \) — Length of the two equal sides
• \( b \) — Length of the base
• \( \theta \) — Vertex angle (between the two equal sides)

Explanation: The formula is derived from the Law of Cosines, simplified for an isosceles triangle where two sides are equal.

3. Importance of Angle Calculation

Details: Calculating angles in isosceles triangles is essential in geometry, trigonometry, architecture, engineering, and various design fields where precise angle measurements are required.

4. Using the Calculator

Tips: Enter the length of the two equal sides and the base in any consistent units. Select whether you want the result in degrees or radians. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Can I use this for equilateral triangles?
A: Yes, but the angle will always be 60° (π/3 radians) regardless of side length.

Q2: What if my triangle isn't isosceles?
A: This calculator only works for isosceles triangles. For scalene triangles, you would need all three side lengths and the full Law of Cosines.

Q3: How precise are the results?
A: Results are precise to 2 decimal places for degrees and 4 decimal places for radians.

Q4: Can I calculate side lengths if I know the angle?
A: No, this calculator only works from side lengths to angle. You would need a different formula for the reverse calculation.

Q5: Does the calculator work for degenerate triangles?
A: No, the calculator checks for valid triangle conditions (sum of any two sides must be greater than the third).