Triangle Calculator Degrees and Sides

This triangle calculator helps you determine the angles and sides of a triangle when you know some of its properties. Whether you have two sides and an angle, two angles and a side, or three sides, this tool will solve the triangle for you.

How to Use This Calculator

Using the triangle calculator is straightforward. Follow these steps:

Enter the known values for your triangle. You can provide:

Two sides and the included angle (SAS)
Two angles and one side (ASA or AAS)
Three sides (SSS)

Select the units for angles (degrees or radians) and sides (meters, feet, etc.).
Click the "Calculate" button to solve the triangle.
Review the results, which will include all angles and sides of the triangle.
Use the "Reset" button to clear all inputs and start over.

Note: The calculator will only solve the triangle if the given values are valid. For example, the sum of angles in a triangle must be 180 degrees, and sides must satisfy the triangle inequality theorem.

Formulas Used

The triangle calculator uses several fundamental formulas to solve triangles based on the given information:

Law of Sines

For any triangle with sides a, b, c and opposite angles A, B, C:

a / sin(A) = b / sin(B) = c / sin(C)

Law of Cosines

For any triangle with sides a, b, c and opposite angles A, B, C:

a² = b² + c² - 2bc cos(A)

b² = a² + c² - 2ac cos(B)

c² = a² + b² - 2ab cos(C)

Triangle Angle Sum

The sum of all angles in a triangle is always 180 degrees (π radians):

A + B + C = 180°

Triangle Inequality Theorem

For any triangle with sides a, b, c:

a + b > c

a + c > b

b + c > a

Worked Examples

Let's look at a few examples to see how the triangle calculator works in practice.

Example 1: SAS Triangle

Given sides a = 5, b = 7, and included angle A = 30°:

Use the Law of Sines to find angle B:

sin(B) / b = sin(A) / a → sin(B) = (b * sin(A)) / a = (7 * sin(30°)) / 5 = 7 * 0.5 / 5 = 0.7 → B ≈ 44.41°

Find angle C using the angle sum: C = 180° - A - B ≈ 180° - 30° - 44.41° ≈ 105.59°
Use the Law of Sines to find side c: c = (a * sin(C)) / sin(A) ≈ (5 * sin(105.59°)) / sin(30°) ≈ 5 * 0.9659 / 0.5 ≈ 9.659

Example 2: ASA Triangle

Given angles A = 40°, B = 60°, and side b = 8:

Find angle C using the angle sum: C = 180° - A - B = 180° - 40° - 60° = 80°
Use the Law of Sines to find side a: a = (b * sin(A)) / sin(B) = (8 * sin(40°)) / sin(60°) ≈ 8 * 0.6428 / 0.8660 ≈ 5.878
Use the Law of Sines to find side c: c = (b * sin(C)) / sin(B) ≈ (8 * sin(80°)) / sin(60°) ≈ 8 * 0.9848 / 0.8660 ≈ 9.123

Example 3: SSS Triangle

Given sides a = 6, b = 8, and c = 10:

Use the Law of Cosines to find angle A: cos(A) = (b² + c² - a²) / (2bc) = (64 + 100 - 36) / (2 * 8 * 10) = 128 / 160 = 0.8 → A ≈ 36.87°
Use the Law of Cosines to find angle B: cos(B) = (a² + c² - b²) / (2ac) = (36 + 100 - 64) / (2 * 6 * 10) = 72 / 120 = 0.6 → B ≈ 53.13°
Find angle C using the angle sum: C = 180° - A - B ≈ 180° - 36.87° - 53.13° ≈ 90°

Frequently Asked Questions

What types of triangles can this calculator solve?

This calculator can solve triangles using the following cases:

Side-Angle-Side (SAS)
Angle-Side-Angle (ASA) or Angle-Angle-Side (AAS)
Side-Side-Side (SSS)

Can I use radians instead of degrees?

Yes, the calculator allows you to select between degrees and radians for angle measurements. The formulas will automatically adjust to the selected unit.

What if I enter invalid values for a triangle?

The calculator will check for validity using the triangle angle sum and inequality theorem. If the values don't form a valid triangle, you'll see an error message explaining the issue.

How accurate are the calculations?

The calculator uses standard trigonometric functions and provides results rounded to four decimal places for precision. For most practical purposes, this level of accuracy is sufficient.

Can I use this calculator for right triangles?

Yes, you can use this calculator for right triangles. Simply enter the known values, and the calculator will determine the other angles and sides, including the hypotenuse if needed.