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Degrees Calculator Triangle

Reviewed by Calculator Editorial Team

Use our degrees calculator triangle to find the interior angles of any triangle. This tool helps you determine the angles when you know two sides and the included angle, or when you know all three sides.

How to Use the Degrees Calculator Triangle

Calculating triangle angles is straightforward with our degrees calculator triangle. Follow these steps:

  1. Enter the known values in the appropriate fields. You can input two sides and the included angle, or all three sides.
  2. Click the "Calculate" button to compute the angles.
  3. Review the results displayed in the result panel.
  4. Use the chart visualization to better understand the angle distribution.

Note: For the most accurate results, ensure your measurements are precise. The calculator uses the Law of Cosines for angle calculations when all three sides are known.

Formula for Triangle Angle Calculation

The degrees calculator triangle uses the following formulas based on the known values:

When two sides and the included angle are known:

c² = a² + b² - 2ab cos(C)

Where:

  • a and b are the known sides
  • C is the known included angle
  • c is the third side

When all three sides are known (Law of Cosines):

cos(A) = (b² + c² - a²) / (2bc)

cos(B) = (a² + c² - b²) / (2ac)

cos(C) = (a² + b² - c²) / (2ab)

Example Calculations

Let's look at a practical example to understand how the degrees calculator triangle works.

Example 1: Two sides and included angle known

Suppose we have a triangle with sides a = 5, b = 7, and included angle C = 60°. We want to find the third side and the other two angles.

  1. Calculate the third side using the formula: c² = 5² + 7² - 2×5×7×cos(60°)
  2. c² = 25 + 49 - 70×0.5 = 74 - 35 = 39
  3. c = √39 ≈ 6.245
  4. Now calculate the other angles using the Law of Sines.

Example 2: All three sides known

For a triangle with sides a = 4, b = 5, and c = 6, we can find all angles using the Law of Cosines.

  1. Calculate angle A: cos(A) = (5² + 6² - 4²) / (2×5×6) = (25 + 36 - 16) / 60 = 45/60 = 0.75
  2. A ≈ arccos(0.75) ≈ 41.41°
  3. Calculate angle B: cos(B) = (4² + 6² - 5²) / (2×4×6) = (16 + 36 - 25) / 48 = 27/48 = 0.5625
  4. B ≈ arccos(0.5625) ≈ 55.77°
  5. Calculate angle C: cos(C) = (4² + 5² - 6²) / (2×4×5) = (16 + 25 - 36) / 40 = 5/40 = 0.125
  6. C ≈ arccos(0.125) ≈ 82.82°

Frequently Asked Questions

What is the difference between degrees and radians in triangle calculations?
Degrees and radians are both units of angular measurement. Degrees are commonly used in everyday contexts, while radians are often used in advanced mathematics and physics. Our degrees calculator triangle uses degrees for all angle calculations.
Can I use this calculator for any type of triangle?
Yes, you can use this calculator for any type of triangle, including scalene, isosceles, and equilateral triangles. The calculator will work as long as you provide the correct measurements.
What if I don't know all the sides or angles?
The degrees calculator triangle can handle cases where you know two sides and the included angle, or when you know all three sides. If you have different information, you may need to use additional geometric principles or tools.