Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 40   b = 60   c = 72.11

Area: T = 12009.99999943
Perimeter: p = 172.11
Semiperimeter: s = 86.055

Angle ∠ A = α = 33.69106107292° = 33°41'26″ = 0.58880120842 rad
Angle ∠ B = β = 56.3111154697° = 56°18'40″ = 0.98328150551 rad
Angle ∠ C = γ = 89.99882345738° = 89°59'54″ = 1.57107655143 rad

Height: ha = 609.9999999715
Height: hb = 409.999999981
Height: hc = 33.28224850764

Median: ma = 63.24549685746
Median: mb = 49.99992604945
Median: mc = 36.0566025502

Inradius: r = 13.94545703263
Circumradius: R = 36.05550000171

Vertex coordinates: A[72.11; 0] B[0; 0] C[22.18772978782; 33.28224850764]
Centroid: CG[31.43224326261; 11.09441616921]
Coordinates of the circumscribed circle: U[36.055; 0.00111109447]
Coordinates of the inscribed circle: I[26.055; 13.94545703263]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3099389271° = 146°18'34″ = 0.58880120842 rad
∠ B' = β' = 123.6898845303° = 123°41'20″ = 0.98328150551 rad
∠ C' = γ' = 90.00217654262° = 90°6″ = 1.57107655143 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 = 40+60+72.11 = 172.11 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 172.11 }{ 2 } = 86.06 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 86.06 * (86.06-40)(86.06-60)(86.06-72.11) } ; ; T = sqrt{ 1440000 } = 1200 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1200 }{ 40 } = 60 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1200 }{ 60 } = 40 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1200 }{ 72.11 } = 33.28 ; ;

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+72.11**2-40**2 }{ 2 * 60 * 72.11 } ) = 33° 41'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 40**2+72.11**2-60**2 }{ 2 * 40 * 72.11 } ) = 56° 18'40" ; ; gamma = 180° - alpha - beta = 180° - 33° 41'26" - 56° 18'40" = 89° 59'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1200 }{ 86.06 } = 13.94 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 40 }{ 2 * sin 33° 41'26" } = 36.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 72.11**2 - 40**2 } }{ 2 } = 63.245 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 72.11**2+2 * 40**2 - 60**2 } }{ 2 } = 49.999 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 40**2 - 72.11**2 } }{ 2 } = 36.056 ; ;
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