Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 13.04   b = 44.12   c = 54

Area: T = 206.9098754425
Perimeter: p = 111.16
Semiperimeter: s = 55.58

Angle ∠ A = α = 10.00325445159° = 10°9″ = 0.17545773354 rad
Angle ∠ B = β = 35.99222204001° = 35°59'32″ = 0.62881827511 rad
Angle ∠ C = γ = 134.0055235084° = 134°19″ = 2.33988325671 rad

Height: ha = 31.73444715376
Height: hb = 9.37993633012
Height: hc = 7.66332872009

Median: ma = 48.87551143221
Median: mb = 32.50219568642
Median: mc = 18.14768454559

Inradius: r = 3.7232719583
Circumradius: R = 37.53877292352

Vertex coordinates: A[54; 0] B[0; 0] C[10.55106222222; 7.66332872009]
Centroid: CG[21.51768740741; 2.5544429067]
Coordinates of the circumscribed circle: U[27; -26.07883649053]
Coordinates of the inscribed circle: I[11.46; 3.7232719583]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.9977455484° = 169°59'51″ = 0.17545773354 rad
∠ B' = β' = 144.00877796° = 144°28″ = 0.62881827511 rad
∠ C' = γ' = 45.9954764916° = 45°59'41″ = 2.33988325671 rad

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How did we calculate this triangle?

a = 13.04 ; ; b = 44.12 ; ; c = 54 ; ;

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

p = a+b+c = 13.04+44.12+54 = 111.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 111.16 }{ 2 } = 55.58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 55.58 * (55.58-13.04)(55.58-44.12)(55.58-54) } ; ; T = sqrt{ 42811.23 } = 206.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 206.91 }{ 13.04 } = 31.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 206.91 }{ 44.12 } = 9.38 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 206.91 }{ 54 } = 7.66 ; ;

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{ 44.12**2+54**2-13.04**2 }{ 2 * 44.12 * 54 } ) = 10° 9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 13.04**2+54**2-44.12**2 }{ 2 * 13.04 * 54 } ) = 35° 59'32" ; ; gamma = 180° - alpha - beta = 180° - 10° 9" - 35° 59'32" = 134° 19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 206.91 }{ 55.58 } = 3.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 13.04 }{ 2 * sin 10° 9" } = 37.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.12**2+2 * 54**2 - 13.04**2 } }{ 2 } = 48.875 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 54**2+2 * 13.04**2 - 44.12**2 } }{ 2 } = 32.502 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 44.12**2+2 * 13.04**2 - 54**2 } }{ 2 } = 18.147 ; ;
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