Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 11.59   b = 6.3   c = 5.3

Area: T = 1.39901165956
Perimeter: p = 23.19
Semiperimeter: s = 11.595

Angle ∠ A = α = 175.2243711463° = 175°13'25″ = 3.05882306926 rad
Angle ∠ B = β = 2.59441371919° = 2°35'39″ = 0.04552762352 rad
Angle ∠ C = γ = 2.18221513449° = 2°10'56″ = 0.03880857257 rad

Height: ha = 0.243988207
Height: hb = 0.44113068557
Height: hc = 0.52545723002

Median: ma = 0.55549549531
Median: mb = 8.44331362656
Median: mc = 8.94435200005

Inradius: r = 0.1219889314
Circumradius: R = 69.59766980798

Vertex coordinates: A[5.3; 0] B[0; 0] C[11.57881226415; 0.52545723002]
Centroid: CG[5.62660408805; 0.17548574334]
Coordinates of the circumscribed circle: U[2.65; 69.54662283924]
Coordinates of the inscribed circle: I[5.295; 0.1219889314]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 4.77662885368° = 4°46'35″ = 3.05882306926 rad
∠ B' = β' = 177.4065862808° = 177°24'21″ = 0.04552762352 rad
∠ C' = γ' = 177.8187848655° = 177°49'4″ = 0.03880857257 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 = 11.59+6.3+5.3 = 23.19 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.19 }{ 2 } = 11.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.6 * (11.6-11.59)(11.6-6.3)(11.6-5.3) } ; ; T = sqrt{ 1.93 } = 1.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.39 }{ 11.59 } = 0.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.39 }{ 6.3 } = 0.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.39 }{ 5.3 } = 0.52 ; ;

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{ 6.3**2+5.3**2-11.59**2 }{ 2 * 6.3 * 5.3 } ) = 175° 13'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.59**2+5.3**2-6.3**2 }{ 2 * 11.59 * 5.3 } ) = 2° 35'39" ; ; gamma = 180° - alpha - beta = 180° - 175° 13'25" - 2° 35'39" = 2° 10'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.39 }{ 11.6 } = 0.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.59 }{ 2 * sin 175° 13'25" } = 69.6 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.3**2+2 * 5.3**2 - 11.59**2 } }{ 2 } = 0.555 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 11.59**2 - 6.3**2 } }{ 2 } = 8.443 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.3**2+2 * 11.59**2 - 5.3**2 } }{ 2 } = 8.944 ; ;
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