7 17 23 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 17   c = 23

Area: T = 35.49991197074
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 10.46218723348° = 10°27'43″ = 0.18325941182 rad
Angle ∠ B = β = 26.16766078821° = 26°10' = 0.45766934616 rad
Angle ∠ C = γ = 143.3721519783° = 143°22'17″ = 2.50223050738 rad

Height: ha = 10.14326056307
Height: hb = 4.17663670244
Height: hc = 3.08768799746

Median: ma = 19.9198584287
Median: mb = 14.72224318643
Median: mc = 6.06221778265

Inradius: r = 1.51106008386
Circumradius: R = 19.27551258521

Vertex coordinates: A[23; 0] B[0; 0] C[6.28326086957; 3.08768799746]
Centroid: CG[9.76108695652; 1.02989599915]
Coordinates of the circumscribed circle: U[11.5; -15.4698693436]
Coordinates of the inscribed circle: I[6.5; 1.51106008386]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.5388127665° = 169°32'17″ = 0.18325941182 rad
∠ B' = β' = 153.8333392118° = 153°50' = 0.45766934616 rad
∠ C' = γ' = 36.62884802169° = 36°37'43″ = 2.50223050738 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 = 7 ; ; b = 17 ; ; c = 23 ; ;

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

p = a+b+c = 7+17+23 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-7)(23.5-17)(23.5-23) } ; ; T = sqrt{ 1260.19 } = 35.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.5 }{ 7 } = 10.14 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.5 }{ 17 } = 4.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.5 }{ 23 } = 3.09 ; ;

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{ 7**2-17**2-23**2 }{ 2 * 17 * 23 } ) = 10° 27'43" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-7**2-23**2 }{ 2 * 7 * 23 } ) = 26° 10' ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-7**2-17**2 }{ 2 * 17 * 7 } ) = 143° 22'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.5 }{ 23.5 } = 1.51 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 10° 27'43" } = 19.28 ; ;




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