Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 7.62   b = 7.81   c = 3.61

Area: T = 13.52203231026
Perimeter: p = 19.04
Semiperimeter: s = 9.52

Angle ∠ A = α = 73.55443716918° = 73°33'16″ = 1.28437659653 rad
Angle ∠ B = β = 79.42111270733° = 79°25'16″ = 1.38661601631 rad
Angle ∠ C = γ = 27.02545012349° = 27°1'28″ = 0.47216665253 rad

Height: ha = 3.54986412343
Height: hb = 3.46223106537
Height: hc = 7.49904837134

Median: ma = 4.74332056671
Median: mb = 4.50554661246
Median: mc = 7.50114815203

Inradius: r = 1.42202020066
Circumradius: R = 3.97325204858

Vertex coordinates: A[3.61; 0] B[0; 0] C[1.39989473684; 7.49904837134]
Centroid: CG[1.67696491228; 2.49768279045]
Coordinates of the circumscribed circle: U[1.805; 3.53987701268]
Coordinates of the inscribed circle: I[1.71; 1.42202020066]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 106.4465628308° = 106°26'44″ = 1.28437659653 rad
∠ B' = β' = 100.5798872927° = 100°34'44″ = 1.38661601631 rad
∠ C' = γ' = 152.9755498765° = 152°58'32″ = 0.47216665253 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 = 7.62+7.81+3.61 = 19.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.04 }{ 2 } = 9.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.52 * (9.52-7.62)(9.52-7.81)(9.52-3.61) } ; ; T = sqrt{ 182.8 } = 13.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.52 }{ 7.62 } = 3.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.52 }{ 7.81 } = 3.46 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.52 }{ 3.61 } = 7.49 ; ;

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{ 7.81**2+3.61**2-7.62**2 }{ 2 * 7.81 * 3.61 } ) = 73° 33'16" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.62**2+3.61**2-7.81**2 }{ 2 * 7.62 * 3.61 } ) = 79° 25'16" ; ; gamma = 180° - alpha - beta = 180° - 73° 33'16" - 79° 25'16" = 27° 1'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.52 }{ 9.52 } = 1.42 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.62 }{ 2 * sin 73° 33'16" } = 3.97 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.81**2+2 * 3.61**2 - 7.62**2 } }{ 2 } = 4.743 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.61**2+2 * 7.62**2 - 7.81**2 } }{ 2 } = 4.505 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.81**2+2 * 7.62**2 - 3.61**2 } }{ 2 } = 7.501 ; ;
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