Triangle Calculator with Degrees and Minutes

This triangle calculator helps you solve for unknown angles, sides, and area of any triangle when you know at least two other measurements. It supports degrees and minutes for angle inputs, making it perfect for surveying, navigation, and engineering applications.

How to Use This Calculator

To use this triangle calculator:

Select the type of triangle you're working with (scalene, isosceles, or equilateral).
Enter the known values in the appropriate fields. You can input angles in degrees and minutes.
Click "Calculate" to see the results.
Review the solution and chart visualization.

The calculator will automatically determine which values to solve for based on the information you provide. For example, if you enter two angles and one side, it will calculate the remaining angles and sides.

Formulas Used

The calculator uses these fundamental triangle formulas:

Angle Sum of a Triangle

For any triangle, the sum of the interior angles is always 180 degrees:

∠A + ∠B + ∠C = 180°

Law of Sines

Relates the lengths of sides to the sines of their opposite angles:

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

Law of Cosines

Relates the lengths of the sides of a triangle to the cosine of one of its angles:

c² = a² + b² - 2ab cos(∠C)

Area of a Triangle

Calculates the area using two sides and the included angle:

Area = (1/2) × a × b × sin(∠C)

The calculator automatically selects the appropriate formulas based on the information you provide.

Worked Examples

Example 1: Solving for Missing Angles

Given a triangle with angles ∠A = 50° and ∠B = 60°, find ∠C.

Using the angle sum formula:

∠C = 180° - ∠A - ∠B = 180° - 50° - 60° = 70°

Example 2: Solving for Missing Sides

Given a triangle with sides a = 5, b = 7, and angle ∠C = 45°, find side c.

Using the Law of Cosines:

c² = 5² + 7² - 2 × 5 × 7 × cos(45°)

c² = 25 + 49 - 70 × 0.7071 ≈ 74 - 49.497 ≈ 24.503

c ≈ √24.503 ≈ 4.95

Example 3: Calculating Area

Given a triangle with sides a = 6, b = 8, and angle ∠C = 30°, find the area.

Using the area formula:

Area = (1/2) × 6 × 8 × sin(30°)

Area = 24 × 0.5 = 12

Practical Applications

This triangle calculator is useful in many real-world scenarios:

Surveying and land measurement
Navigation and route planning
Engineering and construction
Architecture and design
Physics and astronomy
Computer graphics and game development

When working with degrees and minutes, remember that 1 degree = 60 minutes. The calculator automatically converts between these units for accurate calculations.

Frequently Asked Questions

What types of triangles can this calculator solve?

This calculator can solve for any type of triangle: scalene (all sides and angles different), isosceles (two sides and two angles equal), and equilateral (all sides and angles equal).

Can I use degrees and minutes for angle inputs?

Yes, the calculator accepts angles in degrees and minutes format. Simply enter the degrees and minutes separately in the input fields.

What if I don't know any angles?

If you know all three sides of the triangle, the calculator can determine the angles using the Law of Cosines and the Law of Sines.

Is the area calculation accurate?

Yes, the area calculation uses the precise formula (1/2) × a × b × sin(∠C) which provides accurate results for any valid triangle.

Can I save my calculations?

Currently, the calculator does not save calculations. You can bookmark this page or take a screenshot of your results for future reference.