Triangle Solver

Triangle Solver is evaluated from Known Values, Side a and Side b. The calculation reports Side a, Side b and Side c.

Results

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About the Triangle Solver

Triangle Solver is treated here as a quantitative relation between Known Values, Side a, Side b and Side c and Side a, Side b, Side c and Angle A.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
c^2 = a^2 + b^2 - 2ab·cos(C)
a/sin(A) = b/sin(B) = c/sin(C)
Area = sqrt(s(s - a)(s - b)(s - c)) where s = (a+b+c)/2

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

c^2 = a^2 + b^2 - 2ab·cos(C)
a/sin(A) = b/sin(B) = c/sin(C)
Area = sqrt(s(s - a)(s - b)(s - c)) where s = (a+b+c)/2

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: SSS — Property Survey

Inputs

mode: SSS a_val: 150 b_val: 200 c_val: 250
Side a: 150 units. Side b: 200 units. Side c: 250 units. Angle A: 36.8699 deg. Angle B: 53.1301 deg. Angle C: 90 deg. Area: 15,000 sq units. Perimeter: 600 units

With Known Values = SSS, Side a = 150, Side b = 200 and Side c = 250 as the stated inputs, the result is Side a = 150 units, Side b = 200 units and Side c = 250 units. Each value corresponds to the declared output fields.

Example 2: SAS — Staircase Design

Inputs

mode: SAS a_val: 12 b_val: 15 C_ang: 55
Side a: 12 units. Side b: 15 units. Side c: 12.748038 units. Angle A: 0 deg. Angle B: 74.5486 deg. Angle C: 55 deg. Area: 73.7237 sq units. Perimeter: 39.748 units

With Known Values = SAS, Side a = 12, Side b = 15 and Angle C = 55 as the stated inputs, the result is Side a = 12 units, Side b = 15 units and Side c = 12.748038 units. Each value corresponds to the declared output fields.

Example 3: AAS — Navigation Bearing

Inputs

mode: AAS b_val: 50 A_ang: 40 C_ang: 75
Side a: 0 units. Side b: 50 units. Side c: 0 units. Angle A: 40 deg. Angle B: 0 deg. Angle C: 140 deg. Area: 0 sq units. Perimeter: 50 units

With Known Values = AAS, Side b = 50, Angle A = 40 and Angle C = 75 as the stated inputs, the result is Side a = 0 units, Side b = 50 units and Side c = 0 units. Each value corresponds to the declared output fields.

Example 4: Equilateral Triangle — Gazebo Floor

Inputs

mode: SSS a_val: 10 b_val: 10 c_val: 10
Side a: 10 units. Side b: 10 units. Side c: 10 units. Angle A: 60 deg. Angle B: 60 deg. Angle C: 60 deg. Area: 43.3013 sq units. Perimeter: 30 units

With Known Values = SSS, Side a = 10, Side b = 10 and Side c = 10 as the stated inputs, the result is Side a = 10 units, Side b = 10 units and Side c = 10 units. Each value corresponds to the declared output fields.

Common Use Cases

  • Find all angles and sides of a triangle from 3 known values
  • Calculate area of a triangle given 2 sides and included angle
  • Solve surveying problems using trigonometry
  • Determine triangle type from side lengths