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Solving Triangles with Degrees and Minutes Calculator

Reviewed by Calculator Editorial Team

This calculator solves triangles when you know three pieces of information: two sides and one angle, two angles and one side, or all three sides. It handles degrees and minutes for angle measurements and provides precise side length calculations.

How to Use This Calculator

To solve a triangle using this calculator:

  1. Enter the known values in the appropriate fields. You can provide:
    • Two sides and one angle
    • Two angles and one side
    • All three sides
  2. Select the units for angles (degrees and minutes)
  3. Click "Calculate" to solve the triangle
  4. Review the results including all angles and sides
  5. Use the chart visualization to understand the triangle's proportions

The calculator will determine the missing angles and sides using trigonometric principles. All angle measurements are displayed in degrees and minutes for precision.

Formula Used

The calculator uses the following trigonometric relationships to solve triangles:

// For two sides and one angle (SAS): c = (a² + b² - 2ab cos(C))^(1/2) A = arccos((b² + c² - a²)/(2bc)) B = 180° - A - C // For two angles and one side (ASA): b = (a * sin(B)) / sin(A) c = (a * sin(C)) / sin(A) // For three sides (SSS): A = arccos((b² + c² - a²)/(2bc)) B = arccos((a² + c² - b²)/(2ac)) C = 180° - A - B

All angle calculations are converted to degrees and minutes for display. The calculator handles edge cases and provides appropriate error messages when the triangle cannot be solved.

Worked Example

Let's solve a triangle with sides a = 5, b = 7, and angle C = 45° 30'.

Example Input:

  • Side a: 5
  • Side b: 7
  • Angle C: 45° 30'

The calculator will determine:

  • Side c ≈ 8.25
  • Angle A ≈ 32° 15'
  • Angle B ≈ 102° 15'

This example demonstrates how the calculator handles degrees and minutes for angle measurements while calculating all sides and angles of the triangle.

Frequently Asked Questions

What information do I need to solve a triangle?
You need at least three pieces of information: two sides and one angle, two angles and one side, or all three sides. The calculator will determine the missing values.
How does the calculator handle degrees and minutes?
The calculator accepts angle inputs in degrees and minutes, converts them to decimal degrees for calculations, and displays results in degrees and minutes format.
What if the triangle cannot be solved?
The calculator will display an error message if the provided information doesn't form a valid triangle (e.g., angles don't sum to 180° or sides violate triangle inequality).
Can I use this calculator for navigation problems?
Yes, this calculator is useful for navigation problems where you need to determine distances and bearings using angle measurements.