13 20 26 triangle

Obtuse scalene triangle.

Sides: a = 13   b = 20   c = 26

Area: T = 127.218807065
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 29.29546008376° = 29°17'41″ = 0.51112872377 rad
Angle ∠ B = β = 48.83108663768° = 48°49'51″ = 0.85222593949 rad
Angle ∠ C = γ = 101.8754532786° = 101°52'28″ = 1.7788046021 rad

Height: ha = 19.57220108693
Height: hb = 12.7221807065
Height: hc = 9.78660054346

Median: ma = 22.26554440782
Median: mb = 17.95882849961
Median: mc = 10.74770926301

Inradius: r = 4.31224769712
Circumradius: R = 13.28442762931

Vertex coordinates: A[26; 0] B[0; 0] C[8.55876923077; 9.78660054346]
Centroid: CG[11.51992307692; 3.26220018115]
Coordinates of the circumscribed circle: U[13; -2.73334953142]
Coordinates of the inscribed circle: I[9.5; 4.31224769712]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.7055399162° = 150°42'19″ = 0.51112872377 rad
∠ B' = β' = 131.1699133623° = 131°10'9″ = 0.85222593949 rad
∠ C' = γ' = 78.12554672144° = 78°7'32″ = 1.7788046021 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 13+20+26 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-13)(29.5-20)(29.5-26) } ; ; T = sqrt{ 16184.44 } = 127.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 127.22 }{ 13 } = 19.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 127.22 }{ 20 } = 12.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 127.22 }{ 26 } = 9.79 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 29° 17'41" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-13**2-26**2 }{ 2 * 13 * 26 } ) = 48° 49'51" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-13**2-20**2 }{ 2 * 20 * 13 } ) = 101° 52'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 127.22 }{ 29.5 } = 4.31 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 29° 17'41" } = 13.28 ; ;




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