Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 14   b = 14   c = 20

Area: T = 97.98795897113
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 91.16993828056° = 91°10'10″ = 1.5911205907 rad

Height: ha = 13.99770842445
Height: hb = 13.99770842445
Height: hc = 9.79879589711

Median: ma = 15.78797338381
Median: mb = 15.78797338381
Median: mc = 9.79879589711

Inradius: r = 4.08224829046
Circumradius: R = 10.00220831164

Vertex coordinates: A[20; 0] B[0; 0] C[10; 9.79879589711]
Centroid: CG[10; 3.26659863237]
Coordinates of the circumscribed circle: U[10; -0.20441241452]
Coordinates of the inscribed circle: I[10; 4.08224829046]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 88.83106171944° = 88°49'50″ = 1.5911205907 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 = 14+14+20 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-14)(24-14)(24-20) } ; ; T = sqrt{ 9600 } = 97.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97.98 }{ 14 } = 14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97.98 }{ 14 } = 14 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97.98 }{ 20 } = 9.8 ; ;

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{ 14**2+20**2-14**2 }{ 2 * 14 * 20 } ) = 44° 24'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+20**2-14**2 }{ 2 * 14 * 20 } ) = 44° 24'55" ; ; gamma = 180° - alpha - beta = 180° - 44° 24'55" - 44° 24'55" = 91° 10'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97.98 }{ 24 } = 4.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 44° 24'55" } = 10 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 20**2 - 14**2 } }{ 2 } = 15.78 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 14**2 - 14**2 } }{ 2 } = 15.78 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 14**2+2 * 14**2 - 20**2 } }{ 2 } = 9.798 ; ;
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