Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 17   b = 18   c = 28

Area: T = 146.9066220086
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 35.65990876961° = 35°39'33″ = 0.62223684886 rad
Angle ∠ B = β = 38.11658121692° = 38°6'57″ = 0.66552464194 rad
Angle ∠ C = γ = 106.2255100135° = 106°13'30″ = 1.85439777456 rad

Height: ha = 17.2833084716
Height: hb = 16.32329133429
Height: hc = 10.49333014347

Median: ma = 21.94988040676
Median: mb = 21.34224459704
Median: mc = 10.51218980208

Inradius: r = 4.66436895265
Circumradius: R = 14.58107304738

Vertex coordinates: A[28; 0] B[0; 0] C[13.375; 10.49333014347]
Centroid: CG[13.79216666667; 3.49877671449]
Coordinates of the circumscribed circle: U[14; -4.07440276324]
Coordinates of the inscribed circle: I[13.5; 4.66436895265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.3410912304° = 144°20'27″ = 0.62223684886 rad
∠ B' = β' = 141.8844187831° = 141°53'3″ = 0.66552464194 rad
∠ C' = γ' = 73.77548998653° = 73°46'30″ = 1.85439777456 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 = 17+18+28 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-17)(31.5-18)(31.5-28) } ; ; T = sqrt{ 21581.44 } = 146.91 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 146.91 }{ 17 } = 17.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 146.91 }{ 18 } = 16.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 146.91 }{ 28 } = 10.49 ; ;

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{ 18**2+28**2-17**2 }{ 2 * 18 * 28 } ) = 35° 39'33" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 17**2+28**2-18**2 }{ 2 * 17 * 28 } ) = 38° 6'57" ; ;
 gamma = 180° - alpha - beta = 180° - 35° 39'33" - 38° 6'57" = 106° 13'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 146.91 }{ 31.5 } = 4.66 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 17 }{ 2 * sin 35° 39'33" } = 14.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 28**2 - 17**2 } }{ 2 } = 21.949 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 17**2 - 18**2 } }{ 2 } = 21.342 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 17**2 - 28**2 } }{ 2 } = 10.512 ; ;
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