Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.2   b = 8.4   c = 10.09

Area: T = 12.37113311086
Perimeter: p = 21.69
Semiperimeter: s = 10.845

Angle ∠ A = α = 16.97334268223° = 16°58'24″ = 0.29662421834 rad
Angle ∠ B = β = 50.02438007357° = 50°1'26″ = 0.87330800272 rad
Angle ∠ C = γ = 113.0032772442° = 113°10″ = 1.9722270443 rad

Height: ha = 7.73220819429
Height: hb = 2.94655550259
Height: hc = 2.45221964536

Median: ma = 9.14546186361
Median: mb = 6.19554862602
Median: mc = 3.86662611138

Inradius: r = 1.14107405356
Circumradius: R = 5.48108006838

Vertex coordinates: A[10.09; 0] B[0; 0] C[2.05659018831; 2.45221964536]
Centroid: CG[4.0498633961; 0.81773988179]
Coordinates of the circumscribed circle: U[5.045; -2.14217635574]
Coordinates of the inscribed circle: I[2.445; 1.14107405356]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0276573178° = 163°1'36″ = 0.29662421834 rad
∠ B' = β' = 129.9766199264° = 129°58'34″ = 0.87330800272 rad
∠ C' = γ' = 66.9977227558° = 66°59'50″ = 1.9722270443 rad

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How did we calculate this triangle?

a = 3.2 ; ; b = 8.4 ; ; c = 10.09 ; ;

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

p = a+b+c = 3.2+8.4+10.09 = 21.69 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.69 }{ 2 } = 10.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.85 * (10.85-3.2)(10.85-8.4)(10.85-10.09) } ; ; T = sqrt{ 153.05 } = 12.37 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.37 }{ 3.2 } = 7.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.37 }{ 8.4 } = 2.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.37 }{ 10.09 } = 2.45 ; ;

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{ 8.4**2+10.09**2-3.2**2 }{ 2 * 8.4 * 10.09 } ) = 16° 58'24" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.2**2+10.09**2-8.4**2 }{ 2 * 3.2 * 10.09 } ) = 50° 1'26" ; ; gamma = 180° - alpha - beta = 180° - 16° 58'24" - 50° 1'26" = 113° 10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.37 }{ 10.85 } = 1.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.2 }{ 2 * sin 16° 58'24" } = 5.48 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.4**2+2 * 10.09**2 - 3.2**2 } }{ 2 } = 9.145 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 10.09**2+2 * 3.2**2 - 8.4**2 } }{ 2 } = 6.195 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8.4**2+2 * 3.2**2 - 10.09**2 } }{ 2 } = 3.866 ; ;
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