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Welcome to the Teachers' Choice Software web site.
Our FREE on line mathematics 'How-To' library is open 24 hours a day. 
The ever-growing library now has 71 helpful topics, and every topic includes a free download!

The triangle solver data sets both calculate and plot triangles:

Lengths & Angles

If you know three of the six values including internal angles and sides of a triangle, you may be able to solve the triangle and find the unknown angles and sides.

Simply type the known values onto the input triangle, then click 'Apply'. If possible, one or two solutions will be displayed. 

Select the 'display working' option, and the complete worked solution will be displayed on the text view!

Maths Helper Plus created the following solution given two sides and one non-included angle: 

Given: A = 30°, a = 3, b = 5

1. Use the Sine Rule to find the other angle that is
      opposite one of the two given sides, ie angle 'B'
   [sin B]/b = [sin A]/a
ie [sin B]/5 = [sin 30°]/3
    so sin B = 5[sin 30°]/3


sides: a=3, b=5, c=5.98844
angles: A=30°, B=56.4427°, C=93.5573°

Case 2:
Since 'b' > 'a', then 'B' > 'A' ie 'B' > 30°,
so that the alternative value: B = 123.557° is valid.
This triangle has a SECOND solution:

2. Calculate angle 'C'
  'C' = 180° - ('A'+'B')
      = 180° - (30° + 123.557°)
      = 180° - 153.557°
      = 26.4427°
3. Use the Sine Rule to calculate side 'c'
   c/[sin C] = a/[sin A]


 sides: a=3, b=5, c=2.67181
angles: A=30°, B=123.557°, C=26.4427°

3 Points

There is also the option of entering three points that make the vertex of a triangle. The triangle will be solved, and the complete worked solution displayed if required.


Perimeter and area calculations are displayed

Triangle 1:

AREA = (base × perpendicular height) / 2

 Let side 'c' be the base,
  then the perpendicular height = 'b' × sin(A)
                                = 5 × sin(30)
                                = 2.5
 so area = ( 5.98844 × 2.5 ) / 2
         = 7.48555

PERIMETER = a + b + c

          = 3 + 5 + 5.98844
          = 13.9884

The solved triangles can be plotted on the graph view with various line colours and thicknesses, as well as labelling options for the angles and sides. (See picture at the top of this page.)