1. What is the Triangle Angle Formula?

The triangle angle formula calculates the third angle of a triangle when two angles are known. It's based on the fundamental property that the sum of interior angles in any triangle equals 180 degrees.

2. How Does the Calculator Work?

The calculator uses the triangle angle formula:

Where:

• \( \theta \) — The unknown angle (degrees)
• \( \beta \) — First known angle (degrees)
• \( \gamma \) — Second known angle (degrees)

Explanation: The formula simply subtracts the two known angles from 180° to find the third angle.

3. Importance of Angle Calculation

Details: Calculating unknown angles is essential in geometry, trigonometry, and various practical applications like construction, navigation, and engineering.

4. Using the Calculator

Tips: Enter two known angles in degrees (must be between 0° and 179°). The sum of the two angles must be less than 180° to form a valid triangle.

5. Frequently Asked Questions (FAQ)

Q1: Why does the sum of angles equal 180°?
A: This is a fundamental property of Euclidean geometry for plane triangles. The angles always add up to 180° in any triangle.

Q2: Does this work for all types of triangles?
A: Yes, the formula applies to all plane triangles - equilateral, isosceles, scalene, acute, right, and obtuse.

Q3: What if I only know one angle?
A: You need at least two angles to determine the third. With only one angle, there are infinite possible triangles.

Q4: Can I use this for spherical triangles?
A: No, spherical triangles on a sphere's surface have angle sums greater than 180°.

Q5: How precise should my angle measurements be?
A: For most practical purposes, one decimal place is sufficient. The calculator accepts inputs with up to two decimal places.