8 17 23 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 17   c = 23

Area: T = 51.84659255873
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 15.37986321732° = 15°22'43″ = 0.26884077659 rad
Angle ∠ B = β = 34.30111527568° = 34°18'4″ = 0.59986680528 rad
Angle ∠ C = γ = 130.322021507° = 130°19'13″ = 2.27545168349 rad

Height: ha = 12.96114813968
Height: hb = 6.10995206573
Height: hc = 4.50883413554

Median: ma = 19.82442276016
Median: mb = 14.97549791319
Median: mc = 6.65220673478

Inradius: r = 2.16602468995
Circumradius: R = 15.08331524588

Vertex coordinates: A[23; 0] B[0; 0] C[6.60986956522; 4.50883413554]
Centroid: CG[9.87695652174; 1.50327804518]
Coordinates of the circumscribed circle: U[11.5; -9.76596868851]
Coordinates of the inscribed circle: I[7; 2.16602468995]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6211367827° = 164°37'17″ = 0.26884077659 rad
∠ B' = β' = 145.6998847243° = 145°41'56″ = 0.59986680528 rad
∠ C' = γ' = 49.687978493° = 49°40'47″ = 2.27545168349 rad

Calculate another triangle




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 = 8 ; ; b = 17 ; ; c = 23 ; ;

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

p = a+b+c = 8+17+23 = 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 * (24-8)(24-17)(24-23) } ; ; T = sqrt{ 2688 } = 51.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 51.85 }{ 8 } = 12.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 51.85 }{ 17 } = 6.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 51.85 }{ 23 } = 4.51 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 8**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 15° 22'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-8**2-23**2 }{ 2 * 8 * 23 } ) = 34° 18'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-8**2-17**2 }{ 2 * 17 * 8 } ) = 130° 19'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 51.85 }{ 24 } = 2.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 15° 22'43" } = 15.08 ; ;




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