Triangles
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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: 

TRIANGLE SOLUTION
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

Summary

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]

Summary

 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.

Calculations

Perimeter and area calculations are displayed

Calculations:
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
 
Settings

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.)