Finding Degrees of A Triangle Calculator

How to Use the Triangle Angle Calculator

Our triangle angle calculator provides a simple way to determine the angles of a triangle when you know the lengths of its sides. Here's how to use it:

1. Enter the lengths of all three sides of the triangle in the input fields.
2. Click the "Calculate" button to compute the angles.
3. View the results, which include the measures of all three angles in degrees.
4. Use the "Reset" button to clear the inputs and start over.

The calculator uses the Law of Cosines to determine the angles based on the side lengths. This method is reliable for all types of triangles, including scalene, isosceles, and equilateral.

Formula for Finding Triangle Angles

The Law of Cosines is used to find the angles of a triangle when the lengths of all three sides are known. The formula is:

To find an angle, rearrange the formula to solve for the cosine of the angle and then use the inverse cosine function to find the angle in degrees.

For example, to find angle A when sides a, b, and c are known:

Worked Examples

Let's look at two examples to illustrate how to find the angles of a triangle using the Law of Cosines.

Example 1: Scalene Triangle

Given a triangle with sides a = 5, b = 6, and c = 7, find all three angles.

1. Calculate angle A:

   cos(A) = (6² + 7² - 5²) / (2 × 6 × 7) = (36 + 49 - 25) / 84 = 60/84 ≈ 0.7143

   A ≈ cos⁻¹(0.7143) ≈ 44.4°

2. Calculate angle B:

   cos(B) = (5² + 7² - 6²) / (2 × 5 × 7) = (25 + 49 - 36) / 70 = 38/70 ≈ 0.5429

   B ≈ cos⁻¹(0.5429) ≈ 57.1°

3. Calculate angle C:

   cos(C) = (5² + 6² - 7²) / (2 × 5 × 6) = (25 + 36 - 49) / 60 = 12/60 = 0.2

   C ≈ cos⁻¹(0.2) ≈ 78.5°

The angles of the triangle are approximately 44.4°, 57.1°, and 78.5°.

Example 2: Isosceles Triangle

Given a triangle with sides a = 4, b = 4, and c = 6, find all three angles.

1. Calculate angle A:

   cos(A) = (4² + 6² - 4²) / (2 × 4 × 6) = (16 + 36 - 16) / 48 = 36/48 = 0.75

   A ≈ cos⁻¹(0.75) ≈ 41.4°

2. Calculate angle B:

   cos(B) = (4² + 6² - 4²) / (2 × 4 × 6) = same as angle A

   B ≈ 41.4°

3. Calculate angle C:

   cos(C) = (4² + 4² - 6²) / (2 × 4 × 4) = (16 + 16 - 36) / 32 = -4/32 = -0.125

   C ≈ cos⁻¹(-0.125) ≈ 97.2°

The angles of the triangle are approximately 41.4°, 41.4°, and 97.2°.

Types of Triangles Based on Angles

Triangles can be classified based on their angles:

• Acute Triangle: All three angles are less than 90°.
• Right Triangle: One angle is exactly 90°.
• Obtuse Triangle: One angle is greater than 90°.

Our calculator can help you determine the type of triangle based on the calculated angles.