Understanding Triangle Calculations
Triangle Properties
A triangle is a three-sided polygon with three angles that sum to 180 degrees. Understanding triangle properties is fundamental to geometry and has practical applications in construction, engineering, and design.
Calculation Methods
Three Sides (SSS)
When you know all three sides of a triangle, you can calculate:
- Area using Heron's formula
- Perimeter by adding all sides
- Angles using the law of cosines
Two Sides and Angle (SAS)
With two sides and their included angle, you can find:
- Area using the SAS formula
- The third side using the law of cosines
- Remaining angles using the law of sines
Base and Height
The simplest method for area calculation:
- Area = ½ × base × height
- Useful when height is known
- Common in basic geometry problems
Common Applications
- Architecture and Construction
- Land Surveying
- Engineering Design
- Navigation and GPS
- Computer Graphics
Tips for Accurate Measurements
- Always use consistent units of measurement
- Double-check your measurements
- Consider using decimal points for more precise results
- Verify that your triangle is possible (triangle inequality theorem)
- Remember that angles must sum to 180 degrees