9 18 23 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 18   c = 23

Area: T = 74.83331477355
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 21.19331307973° = 21°11'35″ = 0.37698899112 rad
Angle ∠ B = β = 46.30548463945° = 46°18'17″ = 0.80881720292 rad
Angle ∠ C = γ = 112.5022022808° = 112°30'7″ = 1.96435307132 rad

Height: ha = 16.63295883857
Height: hb = 8.31547941928
Height: hc = 6.50772302379

Median: ma = 20.15656443707
Median: mb = 14.96766295471
Median: mc = 8.38215273071

Inradius: r = 2.99333259094
Circumradius: R = 12.44876923421

Vertex coordinates: A[23; 0] B[0; 0] C[6.21773913043; 6.50772302379]
Centroid: CG[9.73991304348; 2.1699076746]
Coordinates of the circumscribed circle: U[11.5; -4.76439316371]
Coordinates of the inscribed circle: I[7; 2.99333259094]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.8076869203° = 158°48'25″ = 0.37698899112 rad
∠ B' = β' = 133.6955153606° = 133°41'43″ = 0.80881720292 rad
∠ C' = γ' = 67.49879771918° = 67°29'53″ = 1.96435307132 rad

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How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 9 ; ; b = 18 ; ; c = 23 ; ;

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

p = a+b+c = 9+18+23 = 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 * (25-9)(25-18)(25-23) } ; ; T = sqrt{ 5600 } = 74.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.83 }{ 9 } = 16.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.83 }{ 18 } = 8.31 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.83 }{ 23 } = 6.51 ; ;

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+23**2-9**2 }{ 2 * 18 * 23 } ) = 21° 11'35" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+23**2-18**2 }{ 2 * 9 * 23 } ) = 46° 18'17" ; ; gamma = 180° - alpha - beta = 180° - 21° 11'35" - 46° 18'17" = 112° 30'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.83 }{ 25 } = 2.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9 }{ 2 * sin 21° 11'35" } = 12.45 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 23**2 - 9**2 } }{ 2 } = 20.156 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 9**2 - 18**2 } }{ 2 } = 14.967 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 9**2 - 23**2 } }{ 2 } = 8.382 ; ;
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