Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 8   b = 18   c = 24

Area: T = 54.54435605732
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 14.62664748646° = 14°37'35″ = 0.25552801443 rad
Angle ∠ B = β = 34.62221618397° = 34°37'20″ = 0.60442707183 rad
Angle ∠ C = γ = 130.7511363296° = 130°45'5″ = 2.2822041791 rad

Height: ha = 13.63658901433
Height: hb = 6.06603956192
Height: hc = 4.54552967144

Median: ma = 20.8332666656
Median: mb = 15.46596248337
Median: mc = 7.07110678119

Inradius: r = 2.18217424229
Circumradius: R = 15.84105500286

Vertex coordinates: A[24; 0] B[0; 0] C[6.58333333333; 4.54552967144]
Centroid: CG[10.19444444444; 1.51550989048]
Coordinates of the circumscribed circle: U[12; -10.34403590465]
Coordinates of the inscribed circle: I[7; 2.18217424229]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.3743525135° = 165°22'25″ = 0.25552801443 rad
∠ B' = β' = 145.378783816° = 145°22'40″ = 0.60442707183 rad
∠ C' = γ' = 49.24986367043° = 49°14'55″ = 2.2822041791 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 = 8+18+24 = 50 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 50 }{ 2 } = 25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25 * (25-8)(25-18)(25-24) } ; ; T = sqrt{ 2975 } = 54.54 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.54 }{ 8 } = 13.64 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.54 }{ 18 } = 6.06 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.54 }{ 24 } = 4.55 ; ;

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+24**2-8**2 }{ 2 * 18 * 24 } ) = 14° 37'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 8**2+24**2-18**2 }{ 2 * 8 * 24 } ) = 34° 37'20" ; ;
 gamma = 180° - alpha - beta = 180° - 14° 37'35" - 34° 37'20" = 130° 45'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.54 }{ 25 } = 2.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 8 }{ 2 * sin 14° 37'35" } = 15.84 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 24**2 - 8**2 } }{ 2 } = 20.833 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24**2+2 * 8**2 - 18**2 } }{ 2 } = 15.46 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 8**2 - 24**2 } }{ 2 } = 7.071 ; ;
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