Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 27.73   b = 25.5   c = 10.63

Area: T = 135.5254992728
Perimeter: p = 63.86
Semiperimeter: s = 31.93

Angle ∠ A = α = 90.60330578539° = 90°36'11″ = 1.58113216719 rad
Angle ∠ B = β = 66.85875760436° = 66°51'27″ = 1.16768848319 rad
Angle ∠ C = γ = 22.53993661025° = 22°32'22″ = 0.39333861498 rad

Height: ha = 9.77546118087
Height: hb = 10.62994111944
Height: hc = 25.49985875312

Median: ma = 13.76217304508
Median: mb = 16.68656944716
Median: mc = 26.10327244747

Inradius: r = 4.24444407369
Circumradius: R = 13.86657680378

Vertex coordinates: A[10.63; 0] B[0; 0] C[10.89883913452; 25.49985875312]
Centroid: CG[7.17661304484; 8.54995291771]
Coordinates of the circumscribed circle: U[5.315; 12.80766505488]
Coordinates of the inscribed circle: I[6.43; 4.24444407369]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.39769421461° = 89°23'49″ = 1.58113216719 rad
∠ B' = β' = 113.1422423956° = 113°8'33″ = 1.16768848319 rad
∠ C' = γ' = 157.4610633898° = 157°27'38″ = 0.39333861498 rad

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How did we calculate this triangle?

a = 27.73 ; ; b = 25.5 ; ; c = 10.63 ; ;

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

p = a+b+c = 27.73+25.5+10.63 = 63.86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63.86 }{ 2 } = 31.93 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.93 * (31.93-27.73)(31.93-25.5)(31.93-10.63) } ; ; T = sqrt{ 18367.02 } = 135.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.52 }{ 27.73 } = 9.77 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.52 }{ 25.5 } = 10.63 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.52 }{ 10.63 } = 25.5 ; ;

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{ 25.5**2+10.63**2-27.73**2 }{ 2 * 25.5 * 10.63 } ) = 90° 36'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 27.73**2+10.63**2-25.5**2 }{ 2 * 27.73 * 10.63 } ) = 66° 51'27" ; ; gamma = 180° - alpha - beta = 180° - 90° 36'11" - 66° 51'27" = 22° 32'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.52 }{ 31.93 } = 4.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 27.73 }{ 2 * sin 90° 36'11" } = 13.87 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.5**2+2 * 10.63**2 - 27.73**2 } }{ 2 } = 13.762 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.63**2+2 * 27.73**2 - 25.5**2 } }{ 2 } = 16.686 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.5**2+2 * 27.73**2 - 10.63**2 } }{ 2 } = 26.103 ; ;
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