Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 20.4   b = 17.7   c = 29.02

Area: T = 178.3287548232
Perimeter: p = 67.12
Semiperimeter: s = 33.56

Angle ∠ A = α = 43.97553566589° = 43°58'31″ = 0.76875147634 rad
Angle ∠ B = β = 37.04655532937° = 37°2'44″ = 0.64765668782 rad
Angle ∠ C = γ = 98.97990900474° = 98°58'45″ = 1.7287511012 rad

Height: ha = 17.48330929639
Height: hb = 20.15500054499
Height: hc = 12.29899757568

Median: ma = 21.76443102349
Median: mb = 23.47699318278
Median: mc = 12.41771212445

Inradius: r = 5.31436933323
Circumradius: R = 14.69900208408

Vertex coordinates: A[29.02; 0] B[0; 0] C[16.2822398346; 12.29899757568]
Centroid: CG[15.10107994487; 4.09766585856]
Coordinates of the circumscribed circle: U[14.51; -2.2932730316]
Coordinates of the inscribed circle: I[15.86; 5.31436933323]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.0254643341° = 136°1'29″ = 0.76875147634 rad
∠ B' = β' = 142.9544446706° = 142°57'16″ = 0.64765668782 rad
∠ C' = γ' = 81.02109099526° = 81°1'15″ = 1.7287511012 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 = 20.4+17.7+29.02 = 67.12 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67.12 }{ 2 } = 33.56 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.56 * (33.56-20.4)(33.56-17.7)(33.56-29.02) } ; ; T = sqrt{ 31800.71 } = 178.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 178.33 }{ 20.4 } = 17.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 178.33 }{ 17.7 } = 20.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 178.33 }{ 29.02 } = 12.29 ; ;

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{ 17.7**2+29.02**2-20.4**2 }{ 2 * 17.7 * 29.02 } ) = 43° 58'31" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 20.4**2+29.02**2-17.7**2 }{ 2 * 20.4 * 29.02 } ) = 37° 2'44" ; ; gamma = 180° - alpha - beta = 180° - 43° 58'31" - 37° 2'44" = 98° 58'45" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 178.33 }{ 33.56 } = 5.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 20.4 }{ 2 * sin 43° 58'31" } = 14.69 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.7**2+2 * 29.02**2 - 20.4**2 } }{ 2 } = 21.764 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.02**2+2 * 20.4**2 - 17.7**2 } }{ 2 } = 23.47 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 17.7**2+2 * 20.4**2 - 29.02**2 } }{ 2 } = 12.417 ; ;
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