Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 119   b = 70   c = 139.93

Area: T = 4162.975533735
Perimeter: p = 328.93
Semiperimeter: s = 164.465

Angle ∠ A = α = 58.21329538663° = 58°12'47″ = 1.01660077123 rad
Angle ∠ B = β = 300.0004595932° = 30°2″ = 0.5243606797 rad
Angle ∠ C = γ = 91.78765865405° = 91°47'12″ = 1.60219781443 rad

Height: ha = 69.96659720563
Height: hb = 118.9422152496
Height: hc = 59.50108266612

Median: ma = 93.27435356358
Median: mb = 125.0832782388
Median: mc = 68.08437629321

Inradius: r = 25.31222265366
Circumradius: R = 69.9999027471

Vertex coordinates: A[139.93; 0] B[0; 0] C[103.0576545773; 59.50108266612]
Centroid: CG[80.99655152576; 19.83436088871]
Coordinates of the circumscribed circle: U[69.965; -2.18223432091]
Coordinates of the inscribed circle: I[94.465; 25.31222265366]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 121.7877046134° = 121°47'13″ = 1.01660077123 rad
∠ B' = β' = 1509.999540407° = 149°59'58″ = 0.5243606797 rad
∠ C' = γ' = 88.21334134595° = 88°12'48″ = 1.60219781443 rad

Calculate another triangle




How did we calculate this triangle?

a = 119 ; ; b = 70 ; ; c = 139.93 ; ;

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

p = a+b+c = 119+70+139.93 = 328.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 328.93 }{ 2 } = 164.47 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 164.47 * (164.47-119)(164.47-70)(164.47-139.93) } ; ; T = sqrt{ 17330363.66 } = 4162.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4162.98 }{ 119 } = 69.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4162.98 }{ 70 } = 118.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4162.98 }{ 139.93 } = 59.5 ; ;

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{ 70**2+139.93**2-119**2 }{ 2 * 70 * 139.93 } ) = 58° 12'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 119**2+139.93**2-70**2 }{ 2 * 119 * 139.93 } ) = 30° 2" ; ; gamma = 180° - alpha - beta = 180° - 58° 12'47" - 30° 2" = 91° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4162.98 }{ 164.47 } = 25.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 119 }{ 2 * sin 58° 12'47" } = 70 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 139.93**2 - 119**2 } }{ 2 } = 93.274 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 139.93**2+2 * 119**2 - 70**2 } }{ 2 } = 125.083 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 70**2+2 * 119**2 - 139.93**2 } }{ 2 } = 68.084 ; ;
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.