Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 24.37   b = 88.43   c = 85

Area: T = 1035.725497173
Perimeter: p = 197.8
Semiperimeter: s = 98.9

Angle ∠ A = α = 15.99768913554° = 15°59'49″ = 0.27991984242 rad
Angle ∠ B = β = 90.01333873169° = 90°48″ = 1.57110299796 rad
Angle ∠ C = γ = 73.99897213277° = 73°59'23″ = 1.29113642498 rad

Height: ha = 854.9999976798
Height: hb = 23.42547420949
Height: hc = 24.37699993348

Median: ma = 85.87217545238
Median: mb = 44.21095264055
Median: mc = 48.99662335287

Inradius: r = 10.47224466302
Circumradius: R = 44.21550012069

Vertex coordinates: A[85; 0] B[0; 0] C[-0.00656941176; 24.37699993348]
Centroid: CG[28.33114352941; 8.12333331116]
Coordinates of the circumscribed circle: U[42.5; 12.1954930575]
Coordinates of the inscribed circle: I[10.47; 10.47224466302]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0033108645° = 164°11″ = 0.27991984242 rad
∠ B' = β' = 89.98766126831° = 89°59'12″ = 1.57110299796 rad
∠ C' = γ' = 106.0110278672° = 106°37″ = 1.29113642498 rad

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How did we calculate this triangle?

a = 24.37 ; ; b = 88.43 ; ; c = 85 ; ;

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

p = a+b+c = 24.37+88.43+85 = 197.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 197.8 }{ 2 } = 98.9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 98.9 * (98.9-24.37)(98.9-88.43)(98.9-85) } ; ; T = sqrt{ 1072726.22 } = 1035.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1035.72 }{ 24.37 } = 85 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1035.72 }{ 88.43 } = 23.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1035.72 }{ 85 } = 24.37 ; ;

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{ 88.43**2+85**2-24.37**2 }{ 2 * 88.43 * 85 } ) = 15° 59'49" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.37**2+85**2-88.43**2 }{ 2 * 24.37 * 85 } ) = 90° 48" ; ; gamma = 180° - alpha - beta = 180° - 15° 59'49" - 90° 48" = 73° 59'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1035.72 }{ 98.9 } = 10.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.37 }{ 2 * sin 15° 59'49" } = 44.22 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 88.43**2+2 * 85**2 - 24.37**2 } }{ 2 } = 85.872 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 85**2+2 * 24.37**2 - 88.43**2 } }{ 2 } = 44.21 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 88.43**2+2 * 24.37**2 - 85**2 } }{ 2 } = 48.996 ; ;
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