Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 138.3   b = 132.15   c = 125

Area: T = 7485.59663016
Perimeter: p = 395.45
Semiperimeter: s = 197.725

Angle ∠ A = α = 65.00109918314° = 65°4″ = 1.13444813245 rad
Angle ∠ B = β = 59.99985313733° = 59°59'55″ = 1.04771719188 rad
Angle ∠ C = γ = 555.0004767953° = 55°2″ = 0.96599394102 rad

Height: ha = 108.2521573414
Height: hb = 113.2899387841
Height: hc = 119.7769540826

Median: ma = 108.4555468972
Median: mb = 114.0621559585
Median: mc = 119.9544183962

Inradius: r = 37.85986233486
Circumradius: R = 76.29879672211

Vertex coordinates: A[125; 0] B[0; 0] C[69.153307; 119.7769540826]
Centroid: CG[64.718769; 39.92331802752]
Coordinates of the circumscribed circle: U[62.5; 43.76221960381]
Coordinates of the inscribed circle: I[65.575; 37.85986233486]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.9999008169° = 114°59'56″ = 1.13444813245 rad
∠ B' = β' = 120.0011468627° = 120°5″ = 1.04771719188 rad
∠ C' = γ' = 1254.999523205° = 124°59'58″ = 0.96599394102 rad

Calculate another triangle


How did we calculate this triangle?

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 138.3+132.15+125 = 395.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 395.45 }{ 2 } = 197.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 197.73 * (197.73-138.3)(197.73-132.15)(197.73-125) } ; ; T = sqrt{ 56034151.99 } = 7485.6 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7485.6 }{ 138.3 } = 108.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7485.6 }{ 132.15 } = 113.29 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7485.6 }{ 125 } = 119.77 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos alpha ; ; alpha = arccos( fraction{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 132.15**2+125**2-138.3**2 }{ 2 * 132.15 * 125 } ) = 65° 4" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 138.3**2+125**2-132.15**2 }{ 2 * 138.3 * 125 } ) = 59° 59'55" ; ; gamma = 180° - alpha - beta = 180° - 65° 4" - 59° 59'55" = 55° 2" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7485.6 }{ 197.73 } = 37.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 138.3 }{ 2 * sin 65° 4" } = 76.3 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 132.15**2+2 * 125**2 - 138.3**2 } }{ 2 } = 108.455 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 125**2+2 * 138.3**2 - 132.15**2 } }{ 2 } = 114.062 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 132.15**2+2 * 138.3**2 - 125**2 } }{ 2 } = 119.954 ; ;
Calculate another triangle

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.