Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 129.06   b = 99.37   c = 93

Area: T = 4597.073291303
Perimeter: p = 321.43
Semiperimeter: s = 160.715

Angle ∠ A = α = 84.20327795331° = 84°12'10″ = 1.47696157422 rad
Angle ∠ B = β = 49.9977297699° = 49°59'50″ = 0.87326174619 rad
Angle ∠ C = γ = 45.87999227678° = 45°48' = 0.79993594495 rad

Height: ha = 71.23993136994
Height: hb = 92.52443617395
Height: hc = 98.86217830758

Median: ma = 71.39773217285
Median: mb = 100.9176512896
Median: mc = 105.3721676697

Inradius: r = 28.60438821082
Circumradius: R = 64.86217281673

Vertex coordinates: A[93; 0] B[0; 0] C[82.96328317204; 98.86217830758]
Centroid: CG[58.65442772401; 32.95439276919]
Coordinates of the circumscribed circle: U[46.5; 45.21993960691]
Coordinates of the inscribed circle: I[61.345; 28.60438821082]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 95.79772204669° = 95°47'50″ = 1.47696157422 rad
∠ B' = β' = 130.0032702301° = 130°10″ = 0.87326174619 rad
∠ C' = γ' = 134.2200077232° = 134°12' = 0.79993594495 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 = 129.06+99.37+93 = 321.43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 321.43 }{ 2 } = 160.72 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 160.72 * (160.72-129.06)(160.72-99.37)(160.72-93) } ; ; T = sqrt{ 21133079.37 } = 4597.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4597.07 }{ 129.06 } = 71.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4597.07 }{ 99.37 } = 92.52 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4597.07 }{ 93 } = 98.86 ; ;

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{ 99.37**2+93**2-129.06**2 }{ 2 * 99.37 * 93 } ) = 84° 12'10" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 129.06**2+93**2-99.37**2 }{ 2 * 129.06 * 93 } ) = 49° 59'50" ; ; gamma = 180° - alpha - beta = 180° - 84° 12'10" - 49° 59'50" = 45° 48' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4597.07 }{ 160.72 } = 28.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 129.06 }{ 2 * sin 84° 12'10" } = 64.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 99.37**2+2 * 93**2 - 129.06**2 } }{ 2 } = 71.397 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 93**2+2 * 129.06**2 - 99.37**2 } }{ 2 } = 100.917 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 99.37**2+2 * 129.06**2 - 93**2 } }{ 2 } = 105.372 ; ;
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