15 17 26 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 17   c = 26

Area: T = 120.8976650078
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 33.16444315181° = 33°9'52″ = 0.57988285245 rad
Angle ∠ B = β = 38.31548799765° = 38°18'54″ = 0.66987208081 rad
Angle ∠ C = γ = 108.5210688505° = 108°31'14″ = 1.8944043321 rad

Height: ha = 16.12195533437
Height: hb = 14.22331353033
Height: hc = 9.32997423137

Median: ma = 20.64658228221
Median: mb = 19.44986503388
Median: mc = 9.38108315196

Inradius: r = 4.16988500027
Circumradius: R = 13.71100573005

Vertex coordinates: A[26; 0] B[0; 0] C[11.76992307692; 9.32997423137]
Centroid: CG[12.59897435897; 3.10999141046]
Coordinates of the circumscribed circle: U[13; -4.35549593778]
Coordinates of the inscribed circle: I[12; 4.16988500027]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.8365568482° = 146°50'8″ = 0.57988285245 rad
∠ B' = β' = 141.6855120024° = 141°41'6″ = 0.66987208081 rad
∠ C' = γ' = 71.47993114946° = 71°28'46″ = 1.8944043321 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 = 15 ; ; b = 17 ; ; c = 26 ; ;

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

p = a+b+c = 15+17+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 * (29-15)(29-17)(29-26) } ; ; T = sqrt{ 14616 } = 120.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 120.9 }{ 15 } = 16.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 120.9 }{ 17 } = 14.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 120.9 }{ 26 } = 9.3 ; ;

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{ 15**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 33° 9'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 38° 18'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-17**2 }{ 2 * 17 * 15 } ) = 108° 31'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 120.9 }{ 29 } = 4.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 33° 9'52" } = 13.71 ; ;




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