Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8.92   b = 7.83   c = 2.01

Area: T = 7.02106921169
Perimeter: p = 18.76
Semiperimeter: s = 9.38

Angle ∠ A = α = 116.8521622806° = 116°51'6″ = 2.03994455543 rad
Angle ∠ B = β = 51.55105726909° = 51°33'2″ = 0.98997272247 rad
Angle ∠ C = γ = 11.59878045032° = 11°35'52″ = 0.20224198746 rad

Height: ha = 1.57441462145
Height: hb = 1.79332802342
Height: hc = 6.98657633004

Median: ma = 3.57553181677
Median: mb = 5.14554858857
Median: mc = 8.33223241056

Inradius: r = 0.74884746393
Circumradius: R = 4.99989955998

Vertex coordinates: A[2.01; 0] B[0; 0] C[5.54766666667; 6.98657633004]
Centroid: CG[2.51988888889; 2.32985877668]
Coordinates of the circumscribed circle: U[1.005; 4.89769308763]
Coordinates of the inscribed circle: I[1.55; 0.74884746393]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 63.14883771942° = 63°8'54″ = 2.03994455543 rad
∠ B' = β' = 128.4499427309° = 128°26'58″ = 0.98997272247 rad
∠ C' = γ' = 168.4022195497° = 168°24'8″ = 0.20224198746 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 = 8.92+7.83+2.01 = 18.76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.76 }{ 2 } = 9.38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.38 * (9.38-8.92)(9.38-7.83)(9.38-2.01) } ; ; T = sqrt{ 49.29 } = 7.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.02 }{ 8.92 } = 1.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.02 }{ 7.83 } = 1.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.02 }{ 2.01 } = 6.99 ; ;

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{ 7.83**2+2.01**2-8.92**2 }{ 2 * 7.83 * 2.01 } ) = 116° 51'6" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8.92**2+2.01**2-7.83**2 }{ 2 * 8.92 * 2.01 } ) = 51° 33'2" ; ; gamma = 180° - alpha - beta = 180° - 116° 51'6" - 51° 33'2" = 11° 35'52" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.02 }{ 9.38 } = 0.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8.92 }{ 2 * sin 116° 51'6" } = 5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.83**2+2 * 2.01**2 - 8.92**2 } }{ 2 } = 3.575 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.01**2+2 * 8.92**2 - 7.83**2 } }{ 2 } = 5.145 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.83**2+2 * 8.92**2 - 2.01**2 } }{ 2 } = 8.332 ; ;
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