Math

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SAS Triangle Calculator.

Solve a triangle from two sides and their included angle.

On-device calculationNo signup
01

Set your values

Results update as you type.

Side c: 6.244998

Side c

0.000000
Angle A (degrees): 43.897886

Angle A (degrees)

0.000000
Angle B (degrees): 76.102114

Angle B (degrees)

0.000000
Angle C (degrees): 60

Angle C (degrees)

0.000000
Area: 15.155445

Area

0.000000
Perimeter: 18.244998

Perimeter

0.000000

Results update automatically as you type.

Use Cases

Construction and Design

Determine the dimensions and angles of triangular components in construction, woodworking, or engineering projects when you know two sides and the included angle.

Example: Find the length of a roof rafter when you know the run and rise and the angle between them.

Navigation and Surveying

Calculate distances or angles in land surveying, navigation, or mapping when you have two known distances and the angle between them.

Example: Determine the distance across a lake when you measure two sides from a point and the angle between them.

Frequently Asked Questions

What is a SAS triangle?
SAS stands for Side-Angle-Side. It refers to a triangle where you know two sides and the angle between them. This calculator uses that information to find the remaining side and angles.
How do I use the SAS Triangle Calculator?
Simply enter the lengths of Side a and Side b, and the measure of the included angle in degrees. The calculator will compute the missing side, the other two angles, and the area of the triangle.
Can I use this calculator for any triangle?
This calculator is specifically for SAS triangles. If you have other combinations like SSS, ASA, or AAS, you'll need a different calculator. For SAS, you must know two sides and the angle between them.

Tips & Common Mistakes

Tips

  • Ensure the included angle is between the two sides you enter. If the angle is not between Side a and Side b, the calculation will be incorrect.
  • The angle must be in degrees. If you have radians, convert to degrees first (multiply by 180/π).
  • Double-check that your side lengths are positive numbers. Negative or zero values will produce invalid results.
  • Use the area result for practical applications like tiling or flooring, but remember it's an estimate.

Common Mistakes to Avoid

  • Entering the angle in radians instead of degrees, which leads to incorrect results.
  • Using the wrong angle: the included angle must be the angle between the two given sides, not any other angle.
  • Confusing Side a and Side b: the calculator uses the given sides and the included angle, so swapping them is fine, but the angle must be between them.

Last updated: August 13, 2026