Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 102   b = 60   c = 119.94

Area: T = 3058.512249275
Perimeter: p = 281.94
Semiperimeter: s = 140.97

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 = 59.97108331911
Height: hb = 101.9550416425
Height: hc = 51.00107085667

Median: ma = 79.94987448307
Median: mb = 107.2143813476
Median: mc = 58.35875110847

Inradius: r = 21.69661941743
Circumradius: R = 59.99991664037

Vertex coordinates: A[119.94; 0] B[0; 0] C[88.3344182091; 51.00107085667]
Centroid: CG[69.42547273637; 177.0002361889]
Coordinates of the circumscribed circle: U[59.97; -1.87105798935]
Coordinates of the inscribed circle: I[80.97; 21.69661941743]

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

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How did we calculate this triangle?

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

p = a+b+c = 102+60+119.94 = 281.94 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 281.94 }{ 2 } = 140.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 140.97 * (140.97-102)(140.97-60)(140.97-119.94) } ; ; T = sqrt{ 9354498.67 } = 3058.51 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3058.51 }{ 102 } = 59.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3058.51 }{ 60 } = 101.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3058.51 }{ 119.94 } = 51 ; ;

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{ 60**2+119.94**2-102**2 }{ 2 * 60 * 119.94 } ) = 58° 12'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 102**2+119.94**2-60**2 }{ 2 * 102 * 119.94 } ) = 30° 2" ; ; gamma = 180° - alpha - beta = 180° - 58° 12'47" - 30° 2" = 91° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3058.51 }{ 140.97 } = 21.7 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 102 }{ 2 * sin 58° 12'47" } = 60 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 119.94**2 - 102**2 } }{ 2 } = 79.949 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 119.94**2+2 * 102**2 - 60**2 } }{ 2 } = 107.214 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 102**2 - 119.94**2 } }{ 2 } = 58.358 ; ;
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