Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 33.43   b = 60.51   c = 69.13

Area: T = 1011.425464986
Perimeter: p = 163.07
Semiperimeter: s = 81.535

Angle ∠ A = α = 28.92195882065° = 28°55'11″ = 0.50547420325 rad
Angle ∠ B = β = 61.08113762358° = 61°4'53″ = 1.0666071127 rad
Angle ∠ C = γ = 89.99990355578° = 89°59'57″ = 1.57107794941 rad

Height: ha = 60.51099999914
Height: hb = 33.43299999953
Height: hc = 29.26215261061

Median: ma = 62.7765929105
Median: mb = 45.08876465897
Median: mc = 34.56554925468

Inradius: r = 12.40547911922
Circumradius: R = 34.56550000049

Vertex coordinates: A[69.13; 0] B[0; 0] C[16.16656422682; 29.26215261061]
Centroid: CG[28.43218807561; 9.75438420354]
Coordinates of the circumscribed circle: U[34.565; 0.0010581822]
Coordinates of the inscribed circle: I[21.025; 12.40547911922]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0880411794° = 151°4'49″ = 0.50547420325 rad
∠ B' = β' = 118.9198623764° = 118°55'7″ = 1.0666071127 rad
∠ C' = γ' = 90.00109644422° = 90°3″ = 1.57107794941 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 = 33.43+60.51+69.13 = 163.07 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 163.07 }{ 2 } = 81.54 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 81.54 * (81.54-33.43)(81.54-60.51)(81.54-69.13) } ; ; T = sqrt{ 1022979.82 } = 1011.42 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1011.42 }{ 33.43 } = 60.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1011.42 }{ 60.51 } = 33.43 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1011.42 }{ 69.13 } = 29.26 ; ;

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{ 60.51**2+69.13**2-33.43**2 }{ 2 * 60.51 * 69.13 } ) = 28° 55'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 33.43**2+69.13**2-60.51**2 }{ 2 * 33.43 * 69.13 } ) = 61° 4'53" ; ; gamma = 180° - alpha - beta = 180° - 28° 55'11" - 61° 4'53" = 89° 59'57" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1011.42 }{ 81.54 } = 12.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 33.43 }{ 2 * sin 28° 55'11" } = 34.57 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 60.51**2+2 * 69.13**2 - 33.43**2 } }{ 2 } = 62.776 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 69.13**2+2 * 33.43**2 - 60.51**2 } }{ 2 } = 45.088 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 60.51**2+2 * 33.43**2 - 69.13**2 } }{ 2 } = 34.565 ; ;
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