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THE FEUTEX TOOLKIT

Triangle from Two Sides and Included Angle

Solve a triangle’s remaining side, angles and area from two sides and their included angle.

Geometry workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaThird Side = sqrt(a**2+b**2-2*a*b*cos(angle*PI/180)); Area = a*b*sin(angle*PI/180)/2; Angle A = atan2(a*sin(angle*PI/180),b-a*cos(angle*PI/180))*180/PI; Angle B = 180-angle-atan2(a*sin(angle*PI/180),b-a*cos(angle*PI/180))*180/PI
Sources and model references

Worked example

Inputs

First side
3 length
Second side
4 length
Included angle
90 degrees

Expected results

Third Side
5 length
Area
6 length²
Angle A
36.86989765 degrees
Angle B
53.13010235 degrees

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "a": 3,
  "b": 4,
  "angle": 90
}

Accuracy and scope

Included angle is between the two supplied sides; unique SAS triangle. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.