Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 218.5   b = 213.3   c = 212.55

Area: T = 19966.49547275
Perimeter: p = 644.35
Semiperimeter: s = 322.175

Angle ∠ A = α = 61.74396445159° = 61°44'23″ = 1.07875600758 rad
Angle ∠ B = β = 59.29989845824° = 59°17'56″ = 1.03549625241 rad
Angle ∠ C = γ = 58.96113709017° = 58°57'41″ = 1.02990700537 rad

Height: ha = 182.7659677139
Height: hb = 187.2155140436
Height: hc = 187.8765744319

Median: ma = 182.7611138511
Median: mb = 187.312164873
Median: mc = 187.9549978385

Inradius: r = 61.97440660432
Circumradius: R = 124.0344239143

Vertex coordinates: A[212.55; 0] B[0; 0] C[111.5576957187; 187.8765744319]
Centroid: CG[108.0365652395; 62.62552481062]
Coordinates of the circumscribed circle: U[106.275; 63.95440214123]
Coordinates of the inscribed circle: I[108.875; 61.97440660432]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 118.2660355484° = 118°15'37″ = 1.07875600758 rad
∠ B' = β' = 120.7011015418° = 120°42'4″ = 1.03549625241 rad
∠ C' = γ' = 121.0398629098° = 121°2'19″ = 1.02990700537 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 = 218.5+213.3+212.55 = 644.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 644.35 }{ 2 } = 322.18 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 322.18 * (322.18-218.5)(322.18-213.3)(322.18-212.55) } ; ; T = sqrt{ 398660911.7 } = 19966.49 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19966.49 }{ 218.5 } = 182.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19966.49 }{ 213.3 } = 187.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19966.49 }{ 212.55 } = 187.88 ; ;

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{ 213.3**2+212.55**2-218.5**2 }{ 2 * 213.3 * 212.55 } ) = 61° 44'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 218.5**2+212.55**2-213.3**2 }{ 2 * 218.5 * 212.55 } ) = 59° 17'56" ; ; gamma = 180° - alpha - beta = 180° - 61° 44'23" - 59° 17'56" = 58° 57'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19966.49 }{ 322.18 } = 61.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 218.5 }{ 2 * sin 61° 44'23" } = 124.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 213.3**2+2 * 212.55**2 - 218.5**2 } }{ 2 } = 182.761 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 212.55**2+2 * 218.5**2 - 213.3**2 } }{ 2 } = 187.312 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 213.3**2+2 * 218.5**2 - 212.55**2 } }{ 2 } = 187.95 ; ;
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