17 20 26 triangle

Acute scalene triangle.

Sides: a = 17   b = 20   c = 26

Area: T = 169.9698930984
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 40.82331687687° = 40°49'23″ = 0.71224987061 rad
Angle ∠ B = β = 50.27222584558° = 50°16'20″ = 0.87774164325 rad
Angle ∠ C = γ = 88.90545727755° = 88°54'16″ = 1.5521677515 rad

Height: ha = 19.99663448217
Height: hb = 16.99768930984
Height: hc = 13.07545331527

Median: ma = 21.58112418549
Median: mb = 19.55876072156
Median: mc = 13.24876412995

Inradius: r = 5.39658390789
Circumradius: R = 13.00223763002

Vertex coordinates: A[26; 0] B[0; 0] C[10.86553846154; 13.07545331527]
Centroid: CG[12.28884615385; 4.35881777176]
Coordinates of the circumscribed circle: U[13; 0.2498574841]
Coordinates of the inscribed circle: I[11.5; 5.39658390789]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.1776831231° = 139°10'37″ = 0.71224987061 rad
∠ B' = β' = 129.7287741544° = 129°43'40″ = 0.87774164325 rad
∠ C' = γ' = 91.09554272245° = 91°5'44″ = 1.5521677515 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 = 17 ; ; b = 20 ; ; c = 26 ; ;

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

p = a+b+c = 17+20+26 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-17)(31.5-20)(31.5-26) } ; ; T = sqrt{ 28889.44 } = 169.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 169.97 }{ 17 } = 20 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 169.97 }{ 20 } = 17 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 169.97 }{ 26 } = 13.07 ; ;

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{ 17**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 40° 49'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 50° 16'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-17**2-20**2 }{ 2 * 20 * 17 } ) = 88° 54'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 169.97 }{ 31.5 } = 5.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 40° 49'23" } = 13 ; ;




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