Triangle Area Calculator by 2 Sides and Included Angle
Calculate triangle area with two sides and the included angle using sine formula. Easy and accurate solution for trigonometry and geometry problems.
Visualization
Formula
Area = (1/2) × A × B × sin(C)This formula uses the Law of Sines to calculate area when you know two sides and the angle between them.
Calculator
Input Values
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Use Cases
- •Construction and architecture projects
- •Land surveying and property measurement
- •Engineering calculations and design
- •Mathematical problem solving and education
Frequently Asked Questions
What is the two sides and angle formula?
The formula is Area = (1/2) × A × B × sin(C), where A and B are the two known sides and C is the angle between them.
When should I use this method?
Use this method when you know the lengths of two sides of a triangle and the measure of the angle between them. This is common in surveying, navigation, and engineering applications.
What angle range is valid?
The included angle must be between 0° and 180°. Angles of 0° or 180° would result in a degenerate triangle (a line), so they're not valid for area calculation.
Can I use any two sides?
Yes, you can use any two sides of the triangle, but you must use the angle that is between those two sides. This is called the included angle.
How accurate is this method?
This method is mathematically exact when the measurements are precise. The accuracy depends on the precision of your side measurements and angle measurements.
Detailed Explanation
Mathematical Background
The formula Area = (1/2) × A × B × sin(C) is derived from the Law of Sines and is one of the fundamental formulas in trigonometry. It's widely used in engineering, surveying, and physics.
Formula Derivation
The formula comes from the standard area formula A = (1/2)bh, where we express the height h in terms of the sides and angle using trigonometry: h = A × sin(C).
Accuracy and Applications
This method is particularly useful in real-world applications where you can easily measure two sides and an angle, such as in surveying, navigation, and engineering design.