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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:
Given: A = 30°, a = 3, b = 5
1. Use the Sine
Rule to find the other angle that is
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°
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' = 180° - ('A'+'B')
= 180° - (30° + 123.557°)
= 180° - 153.557°
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°
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
AREA = (base × perpendicular height) / 2
Let side 'c' be the base,
then the perpendicular height = 'b' × sin(A)
= 5 × sin(30)
so area = ( 5.98844 × 2.5 ) / 2
PERIMETER = a + b + c
= 3 + 5 + 5.98844
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.)