Area of Triangle with Angle

Triangle Area Formula:

\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]

Area (square meters):

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1. What is Area of Triangle with Angle?

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

Purpose: It's useful in geometry, trigonometry, and various practical applications like construction and land surveying.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ \text{Area} = \frac{1}{2} \times a \times b \times \sin(C) \]

Where:

\( a \) — Length of first side (meters)
\( b \) — Length of second side (meters)
\( C \) — Included angle between sides a and b (degrees)

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

3. Importance of Triangle Area Calculation

Details: Accurate area calculations are essential for material estimation, land measurement, and structural design.

4. Using the Calculator

Tips: Enter the lengths of two sides in meters and the included angle in degrees (must be between 0 and 180). All values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What if my angle is 90 degrees?
A: When angle C is 90°, sin(90°) = 1, so the formula simplifies to the standard right triangle area formula (1/2 × base × height).

Q2: Can I use this for any triangle?
A: Yes, as long as you know two sides and the included angle between them.

Q3: What units should I use?
A: The calculator uses meters for sides and degrees for angles, but any consistent units will work (just remember your area units will be squared).

Q4: Why does the angle need to be between 0 and 180 degrees?
A: This is the valid range for an angle in a triangle - angles outside this range wouldn't form a valid triangle.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise, though real-world measurements may introduce some error.