Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 1275   b = 300   c = 1309.82

Area: T = 1912509.999998
Perimeter: p = 2884.82
Semiperimeter: s = 1442.41

Angle ∠ A = α = 76.75992364963° = 76°45'33″ = 1.34397014082 rad
Angle ∠ B = β = 13.24105064292° = 13°14'26″ = 0.23110904318 rad
Angle ∠ C = γ = 900.0002570746° = 90°1″ = 1.57108008136 rad

Height: ha = 3009.999999997
Height: hb = 12754.99999999
Height: hc = 292.0254858375

Median: ma = 704.5622251472
Median: mb = 1283.794387606
Median: mc = 654.9098689742

Inradius: r = 132.5910594906
Circumradius: R = 654.9110000007

Vertex coordinates: A[1309.82; 0] B[0; 0] C[1241.107695836; 292.0254858375]
Centroid: CG[850.309898612; 97.34216194582]
Coordinates of the circumscribed circle: U[654.91; -0.00329384485]
Coordinates of the inscribed circle: I[1142.41; 132.5910594906]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.2410763504° = 103°14'27″ = 1.34397014082 rad
∠ B' = β' = 166.7599493571° = 166°45'34″ = 0.23110904318 rad
∠ C' = γ' = 909.9997429254° = 89°59'59″ = 1.57108008136 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 = 1275+300+1309.82 = 2884.82 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2884.82 }{ 2 } = 1442.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1442.41 * (1442.41-1275)(1442.41-300)(1442.41-1309.82) } ; ; T = sqrt{ 36576562499.3 } = 191250 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 191250 }{ 1275 } = 300 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 191250 }{ 300 } = 1275 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 191250 }{ 1309.82 } = 292.02 ; ;

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{ 300**2+1309.82**2-1275**2 }{ 2 * 300 * 1309.82 } ) = 76° 45'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1275**2+1309.82**2-300**2 }{ 2 * 1275 * 1309.82 } ) = 13° 14'26" ; ; gamma = 180° - alpha - beta = 180° - 76° 45'33" - 13° 14'26" = 90° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 191250 }{ 1442.41 } = 132.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1275 }{ 2 * sin 76° 45'33" } = 654.91 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 300**2+2 * 1309.82**2 - 1275**2 } }{ 2 } = 704.562 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1309.82**2+2 * 1275**2 - 300**2 } }{ 2 } = 1283.794 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 300**2+2 * 1275**2 - 1309.82**2 } }{ 2 } = 654.909 ; ;
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