Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 113.52   b = 500   c = 400

Area: T = 11992.44223106
Perimeter: p = 1013.52
Semiperimeter: s = 506.76

Angle ∠ A = α = 6.88877408439° = 6°53'16″ = 0.12202137557 rad
Angle ∠ B = β = 148.1165520205° = 148°6'56″ = 2.58551035009 rad
Angle ∠ C = γ = 24.99767389515° = 24°59'48″ = 0.4366275397 rad

Height: ha = 211.2833338806
Height: hb = 47.97697692426
Height: hc = 59.96222115532

Median: ma = 449.1977398033
Median: mb = 154.7376534794
Median: mc = 302.3966089922

Inradius: r = 23.66549347041
Circumradius: R = 473.2988086659

Vertex coordinates: A[400; 0] B[0; 0] C[-96.3921512; 59.96222115532]
Centroid: CG[101.2032829333; 19.98774038511]
Coordinates of the circumscribed circle: U[200; 428.965512543]
Coordinates of the inscribed circle: I[6.76; 23.66549347041]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 173.1122259156° = 173°6'44″ = 0.12202137557 rad
∠ B' = β' = 31.88444797954° = 31°53'4″ = 2.58551035009 rad
∠ C' = γ' = 155.0033261048° = 155°12″ = 0.4366275397 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 = 113.52+500+400 = 1013.52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1013.52 }{ 2 } = 506.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 506.76 * (506.76-113.52)(506.76-500)(506.76-400) } ; ; T = sqrt{ 143818672.57 } = 11992.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11992.44 }{ 113.52 } = 211.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11992.44 }{ 500 } = 47.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11992.44 }{ 400 } = 59.96 ; ;

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{ 500**2+400**2-113.52**2 }{ 2 * 500 * 400 } ) = 6° 53'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 113.52**2+400**2-500**2 }{ 2 * 113.52 * 400 } ) = 148° 6'56" ; ; gamma = 180° - alpha - beta = 180° - 6° 53'16" - 148° 6'56" = 24° 59'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11992.44 }{ 506.76 } = 23.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 113.52 }{ 2 * sin 6° 53'16" } = 473.3 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 500**2+2 * 400**2 - 113.52**2 } }{ 2 } = 449.197 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 400**2+2 * 113.52**2 - 500**2 } }{ 2 } = 154.737 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 500**2+2 * 113.52**2 - 400**2 } }{ 2 } = 302.396 ; ;
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