13 16 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 16   c = 26

Area: T = 82.93663460734
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 23.4998960633° = 23°29'56″ = 0.41101342338 rad
Angle ∠ B = β = 29.39897316548° = 29°23'23″ = 0.51329475837 rad
Angle ∠ C = γ = 127.1111307712° = 127°6'41″ = 2.21985108361 rad

Height: ha = 12.75994378574
Height: hb = 10.36770432592
Height: hc = 6.38797189287

Median: ma = 20.58551888502
Median: mb = 18.93440962288
Median: mc = 6.59554529791

Inradius: r = 3.01658671299
Circumradius: R = 16.30216586094

Vertex coordinates: A[26; 0] B[0; 0] C[11.32769230769; 6.38797189287]
Centroid: CG[12.44223076923; 2.12765729762]
Coordinates of the circumscribed circle: U[13; -9.83658565167]
Coordinates of the inscribed circle: I[11.5; 3.01658671299]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.5011039367° = 156°30'4″ = 0.41101342338 rad
∠ B' = β' = 150.6110268345° = 150°36'37″ = 0.51329475837 rad
∠ C' = γ' = 52.88986922878° = 52°53'19″ = 2.21985108361 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 = 13 ; ; b = 16 ; ; c = 26 ; ;

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

p = a+b+c = 13+16+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-13)(27.5-16)(27.5-26) } ; ; T = sqrt{ 6878.44 } = 82.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 82.94 }{ 13 } = 12.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 82.94 }{ 16 } = 10.37 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 82.94 }{ 26 } = 6.38 ; ;

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{ 13**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 23° 29'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 29° 23'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-16**2 }{ 2 * 16 * 13 } ) = 127° 6'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 82.94 }{ 27.5 } = 3.02 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 23° 29'56" } = 16.3 ; ;




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