Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 14.14   b = 9.85   c = 5.39

Area: T = 19.07702504965
Perimeter: p = 29.38
Semiperimeter: s = 14.69

Angle ∠ A = α = 134.0788132152° = 134°4'41″ = 2.3440104861 rad
Angle ∠ B = β = 30.02988249123° = 30°1'44″ = 0.52441018652 rad
Angle ∠ C = γ = 15.89330429359° = 15°53'35″ = 0.27773859274 rad

Height: ha = 2.69773480193
Height: hb = 3.87221320805
Height: hc = 7.0766159739

Median: ma = 3.61328105403
Median: mb = 9.49994855124
Median: mc = 11.88435190495

Inradius: r = 1.29881790672
Circumradius: R = 9.84114256559

Vertex coordinates: A[5.39; 0] B[0; 0] C[12.24220408163; 7.0766159739]
Centroid: CG[5.87773469388; 2.3598719913]
Coordinates of the circumscribed circle: U[2.695; 9.46552329047]
Coordinates of the inscribed circle: I[4.84; 1.29881790672]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 45.92218678482° = 45°55'19″ = 2.3440104861 rad
∠ B' = β' = 149.9711175088° = 149°58'16″ = 0.52441018652 rad
∠ C' = γ' = 164.1076957064° = 164°6'25″ = 0.27773859274 rad

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How did we calculate this triangle?

a = 14.14 ; ; b = 9.85 ; ; c = 5.39 ; ;

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

p = a+b+c = 14.14+9.85+5.39 = 29.38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.38 }{ 2 } = 14.69 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.69 * (14.69-14.14)(14.69-9.85)(14.69-5.39) } ; ; T = sqrt{ 363.67 } = 19.07 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.07 }{ 14.14 } = 2.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.07 }{ 9.85 } = 3.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.07 }{ 5.39 } = 7.08 ; ;

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{ 9.85**2+5.39**2-14.14**2 }{ 2 * 9.85 * 5.39 } ) = 134° 4'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14.14**2+5.39**2-9.85**2 }{ 2 * 14.14 * 5.39 } ) = 30° 1'44" ; ; gamma = 180° - alpha - beta = 180° - 134° 4'41" - 30° 1'44" = 15° 53'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.07 }{ 14.69 } = 1.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14.14 }{ 2 * sin 134° 4'41" } = 9.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.85**2+2 * 5.39**2 - 14.14**2 } }{ 2 } = 3.613 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.39**2+2 * 14.14**2 - 9.85**2 } }{ 2 } = 9.499 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.85**2+2 * 14.14**2 - 5.39**2 } }{ 2 } = 11.884 ; ;
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