Triangle Degrees Calculator

Triangles are fundamental shapes in geometry with three sides and three angles that always sum to 180 degrees. This triangle degrees calculator helps you determine the angles of any triangle when you know at least two sides or one angle and two sides.

How to Use This Calculator

To calculate the angles of a triangle:

Enter the lengths of at least two sides of the triangle in the input fields.
If you know one angle, enter it in the angle field.
Click the "Calculate" button to see the results.
Review the calculated angles and the triangle type.

The calculator will determine all three angles of the triangle using the Law of Cosines and Law of Sines when needed.

Formula Explained

The triangle degrees calculator uses these fundamental geometric principles:

Law of Cosines

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

c² = a² + b² - 2ab cos(C)

This allows calculation of an angle when two sides and the included angle are known.

Law of Sines

For any triangle:

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

This enables angle calculation when two sides and a non-included angle are known.

The calculator automatically selects the appropriate formula based on the information provided.

Worked Examples

Example 1: Two sides and included angle

Given sides a = 5, b = 7, and angle C = 60°:

Calculate side c using Law of Cosines: c² = 5² + 7² - 2×5×7×cos(60°) = 25 + 49 - 35 = 39 → c ≈ 6.24
Calculate angle A: sin(A)/5 = sin(60°)/6.24 → A ≈ 38.94°
Calculate angle B: 180° - 60° - 38.94° ≈ 81.06°

Example 2: Two sides and opposite angle

Given sides a = 4, b = 6, and angle A = 45°:

Calculate angle B using Law of Sines: sin(B)/6 = sin(45°)/4 → B ≈ 75.52°
Calculate angle C: 180° - 45° - 75.52° ≈ 59.48°
Calculate side c using Law of Sines: c = 6 × sin(59.48°)/sin(75.52°) ≈ 5.24

Comparison of Triangle Types
Type	Angle Properties	Side Properties
Acute	All angles < 90°	All sides shorter than the sum of the other two
Right	One angle = 90°	Sides satisfy Pythagorean theorem
Obtuse	One angle > 90°	One side longer than the sum of the other two

Frequently Asked Questions

What is the sum of angles in a triangle?

The sum of all interior angles in any triangle is always 180 degrees. This is a fundamental property of Euclidean geometry.

Can a triangle have two right angles?

No, a triangle cannot have two right angles (90° each) because the sum would be 180°, leaving no degree for the third angle. This would create a straight line rather than a triangle.

How does the calculator determine triangle type?

The calculator examines the calculated angles. If all angles are less than 90°, it's acute; if one angle is exactly 90°, it's right; and if one angle is greater than 90°, it's obtuse.

What if I only know one side and one angle?

With only one side and one angle, you cannot uniquely determine the other sides and angles. You would need at least two sides or another angle to solve the triangle.