9 23 26 triangle

Obtuse scalene triangle.

Sides: a = 9   b = 23   c = 26

Area: T = 102.1766318196
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 19.98221160425° = 19°58'56″ = 0.34987537165 rad
Angle ∠ B = β = 60.84546345737° = 60°50'41″ = 1.06219392055 rad
Angle ∠ C = γ = 99.17332493838° = 99°10'24″ = 1.73108997316 rad

Height: ha = 22.70658484879
Height: hb = 8.88548972344
Height: hc = 7.86597167843

Median: ma = 24.1329857024
Median: mb = 15.69223548265
Median: mc = 11.66219037897

Inradius: r = 3.52333213171
Circumradius: R = 13.16884134226

Vertex coordinates: A[26; 0] B[0; 0] C[4.38546153846; 7.86597167843]
Centroid: CG[10.12882051282; 2.62199055948]
Coordinates of the circumscribed circle: U[13; -2.09993122848]
Coordinates of the inscribed circle: I[6; 3.52333213171]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.0187883958° = 160°1'4″ = 0.34987537165 rad
∠ B' = β' = 119.1555365426° = 119°9'19″ = 1.06219392055 rad
∠ C' = γ' = 80.82767506162° = 80°49'36″ = 1.73108997316 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 = 23 ; ; c = 26 ; ;

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

p = a+b+c = 9+23+26 = 58 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 58 }{ 2 } = 29 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29 * (29-9)(29-23)(29-26) } ; ; T = sqrt{ 10440 } = 102.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.18 }{ 9 } = 22.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.18 }{ 23 } = 8.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.18 }{ 26 } = 7.86 ; ;

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{ 9**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 19° 58'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-9**2-26**2 }{ 2 * 9 * 26 } ) = 60° 50'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-9**2-23**2 }{ 2 * 23 * 9 } ) = 99° 10'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.18 }{ 29 } = 3.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9 }{ 2 * sin 19° 58'56" } = 13.17 ; ;




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