Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 6   b = 23   c = 26

Area: T = 63.17438672237
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 12.19875989742° = 12°11'51″ = 0.21328882629 rad
Angle ∠ B = β = 54.08882502205° = 54°5'18″ = 0.9444018053 rad
Angle ∠ C = γ = 113.7144150805° = 113°42'51″ = 1.98546863377 rad

Height: ha = 21.05879557412
Height: hb = 5.49333797586
Height: hc = 4.8659528248

Median: ma = 24.36218554302
Median: mb = 14.95882753017
Median: mc = 10.65436378763

Inradius: r = 2.29772315354
Circumradius: R = 14.19989091284

Vertex coordinates: A[26; 0] B[0; 0] C[3.51992307692; 4.8659528248]
Centroid: CG[9.84397435897; 1.62198427493]
Coordinates of the circumscribed circle: U[13; -5.71104308451]
Coordinates of the inscribed circle: I[4.5; 2.29772315354]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.8022401026° = 167°48'9″ = 0.21328882629 rad
∠ B' = β' = 125.912174978° = 125°54'42″ = 0.9444018053 rad
∠ C' = γ' = 66.28658491947° = 66°17'9″ = 1.98546863377 rad

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How did we calculate this triangle?

a = 6 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 6+23+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-6)(27.5-23)(27.5-26) } ; ; T = sqrt{ 3990.94 } = 63.17 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.17 }{ 6 } = 21.06 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.17 }{ 23 } = 5.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.17 }{ 26 } = 4.86 ; ;

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{ 23**2+26**2-6**2 }{ 2 * 23 * 26 } ) = 12° 11'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+26**2-23**2 }{ 2 * 6 * 26 } ) = 54° 5'18" ; ; gamma = 180° - alpha - beta = 180° - 12° 11'51" - 54° 5'18" = 113° 42'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.17 }{ 27.5 } = 2.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 12° 11'51" } = 14.2 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 26**2 - 6**2 } }{ 2 } = 24.362 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 26**2+2 * 6**2 - 23**2 } }{ 2 } = 14.958 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 6**2 - 26**2 } }{ 2 } = 10.654 ; ;
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