14 17 26 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 17   c = 26

Area: T = 1098.999713302
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 29.55218752166° = 29°33'7″ = 0.51657775227 rad
Angle ∠ B = β = 36.79111224225° = 36°47'28″ = 0.64221262218 rad
Angle ∠ C = γ = 113.6577002361° = 113°39'25″ = 1.98436889091 rad

Height: ha = 15.57113876146
Height: hb = 12.82334956826
Height: hc = 8.3854593331

Median: ma = 20.82106628137
Median: mb = 19.07222311228
Median: mc = 8.57332140997

Inradius: r = 3.82545513439
Circumradius: R = 14.19326978809

Vertex coordinates: A[26; 0] B[0; 0] C[11.21215384615; 8.3854593331]
Centroid: CG[12.40438461538; 2.79548644437]
Coordinates of the circumscribed circle: U[13; -5.69549691077]
Coordinates of the inscribed circle: I[11.5; 3.82545513439]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.4488124783° = 150°26'53″ = 0.51657775227 rad
∠ B' = β' = 143.2098877577° = 143°12'32″ = 0.64221262218 rad
∠ C' = γ' = 66.34329976391° = 66°20'35″ = 1.98436889091 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 = 14 ; ; b = 17 ; ; c = 26 ; ;

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

p = a+b+c = 14+17+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-14)(28.5-17)(28.5-26) } ; ; T = sqrt{ 11880.94 } = 109 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109 }{ 14 } = 15.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109 }{ 17 } = 12.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109 }{ 26 } = 8.38 ; ;

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{ 14**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 29° 33'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 36° 47'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-17**2 }{ 2 * 17 * 14 } ) = 113° 39'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109 }{ 28.5 } = 3.82 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 29° 33'7" } = 14.19 ; ;




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