1. What is the Area of a Triangle Calculator?

Definition: This calculator computes the area of a triangle when two sides and the included angle are known.

Purpose: It helps students, engineers, and designers quickly determine triangle areas, especially for non-right triangles.

2. How Does the Calculator Work?

The calculator uses the trigonometric formula:

Where:

• \( a \) — Length of side a (meters)
• \( b \) — Length of side b (meters)
• \( C \) — Included angle between sides a and b (degrees)
• Area — Result in square meters

Explanation: The formula calculates area using half the product of two sides multiplied by the sine of their included angle.

3. Importance of Triangle Area Calculation

Details: Accurate area calculations are essential in construction, land surveying, engineering, and various design fields.

4. Using the Calculator

Tips: Enter lengths of two sides and their included angle (must be between 0° and 180°). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for right triangles?
A: Yes, when C=90°, sin(90°)=1, simplifying to the standard right triangle formula (1/2)ab.

Q2: Why does the angle need to be between 0° and 180°?
A: This is the valid range for an angle in a Euclidean triangle.

Q3: What units should I use?
A: The calculator uses meters for sides, but any consistent unit can be used (results will be in squared units).

Q4: How accurate is the calculation?
A: Very accurate, using PHP's built-in trigonometric functions with double precision.

Q5: Can I use this for acute triangles?
A: Yes, the formula works for all triangle types - acute, right, and obtuse.