Triangle Angle and Side Length Calculator: Instantly Solve Triangle Measurements
Introduction
Triangles are one of the most essential shapes in geometry, playing a crucial role in mathematics, construction, engineering, and navigation. Whether you’re solving a school assignment, designing a roof, or working on a bridge, knowing how to calculate missing angles and side lengths is necessary.
A Triangle Angle & Side Length Calculator instantly finds unknown values using formulas such as the Pythagorean Theorem, Sine Rule, and Cosine Rule. Instead of manual calculations, this tool delivers fast and accurate results.
Types of Triangles
A triangle is a three-sided polygon with three angles that always sum to 180°.
Triangles by Sides:
- Equilateral Triangle – All sides are equal, and each angle is 60°.
- Isosceles Triangle – Two sides are equal, and two angles are equal.
- Scalene Triangle – No sides or angles are equal.
Triangles by Angles:
- Acute Triangle – All angles are less than 90°.
- Right Triangle – One angle is exactly 90°.
- Obtuse Triangle – One angle is greater than 90°.
How to Calculate Triangle Angles and Side Lengths
1. Pythagorean Theorem (Right Triangles Only)
For a right triangle, if two sides are known, the third side can be calculated using:
Formula:
c² = a² + b²
- a and b = triangle legs
- c = hypotenuse (longest side)
Example Calculation:
If a = 3 cm and b = 4 cm, find c:
c² = 3² + 4²
c² = 9 + 16
c² = 25
c = √25 = 5 cm
2. Sine Rule (For Any Triangle)
If two angles and one side or two sides and one opposite angle are known, use the Sine Rule:
Formula:
a / sin(A) = b / sin(B) = c / sin(C)
- a, b, c = triangle sides
- A, B, C = opposite angles
Example Calculation:
If A = 40°, B = 60°, and a = 10 cm, find b:
3. Cosine Rule (For Any Triangle)
If two sides and the included angle are known, use the Cosine Rule to find the third side:
Formula:
Example Calculation:
If a = 8 cm, b = 10 cm, and C = 45°, find c:
4. Heron’s Formula (Area of a Triangle)
If all three sides are known, Heron’s Formula calculates the area:
Formula:
Where:
- s = semi-perimeter
- a, b, c = triangle sides
Example Calculation:
If a = 7 cm, b = 10 cm, and c = 12 cm:
How to Use the Triangle Angle & Side Length Calculator
1️⃣ Select what you want to calculate (sides, angles, or area).
2️⃣ Enter the known values into the calculator.
3️⃣ Click “Calculate”.
4️⃣ Instantly view the missing sides, angles, or area.
Benefits of Using a Triangle Calculator
✔️ Instant and Accurate Results – No manual calculations required.
✔️ Works for Any Triangle Type – Right, isosceles, scalene, and equilateral.
✔️ Perfect for Students & Engineers – Great for geometry assignments and real-world applications.
Conclusion(Triangle Angle and Side Length Calculator)
A Triangle Angle & Side Length Calculator is an essential tool for students, architects, engineers, and professionals who need fast and accurate calculations. Instead of manually solving equations, use this calculator to save time and ensure precision.[Triangle Angle and Side Length Calculator]
Try our Triangle Calculator today for instant results! 🚀[Triangle Angle and Side Length Calculator]
Frequently Asked Questions (FAQs)
1. Can this calculator solve any type of triangle?
Yes! It works for right, acute, obtuse, scalene, isosceles, and equilateral triangles.
2. What if I only know two sides and one angle?
The calculator uses the Sine Rule or Cosine Rule to find missing values.
3. Is this calculator free?
Yes! Our Triangle Angle & Side Length Calculator is completely free to use online.
4. Can I calculate the area with this tool?
Yes! The calculator includes Heron’s Formula for finding area.