12 21 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 21   c = 26

Area: T = 123.9299163234
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 26.99875872637° = 26°59'51″ = 0.47111967878 rad
Angle ∠ B = β = 52.66002917273° = 52°36'1″ = 0.91880482782 rad
Angle ∠ C = γ = 100.4022121009° = 100°24'8″ = 1.75223475876 rad

Height: ha = 20.65548605391
Height: hb = 11.80327774509
Height: hc = 9.53330125565

Median: ma = 22.85882589013
Median: mb = 17.31332896932
Median: mc = 11.11330553854

Inradius: r = 4.20109885842
Circumradius: R = 13.2177227949

Vertex coordinates: A[26; 0] B[0; 0] C[7.28884615385; 9.53330125565]
Centroid: CG[11.09661538462; 3.17876708522]
Coordinates of the circumscribed circle: U[13; -2.38664439352]
Coordinates of the inscribed circle: I[8.5; 4.20109885842]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.0022412736° = 153°9″ = 0.47111967878 rad
∠ B' = β' = 127.4399708273° = 127°23'59″ = 0.91880482782 rad
∠ C' = γ' = 79.5987878991° = 79°35'52″ = 1.75223475876 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 = 12 ; ; b = 21 ; ; c = 26 ; ;

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

p = a+b+c = 12+21+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 * (29.5-12)(29.5-21)(29.5-26) } ; ; T = sqrt{ 15358.44 } = 123.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 123.93 }{ 12 } = 20.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 123.93 }{ 21 } = 11.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 123.93 }{ 26 } = 9.53 ; ;

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{ 12**2-21**2-26**2 }{ 2 * 21 * 26 } ) = 26° 59'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 21**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 52° 36'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-21**2 }{ 2 * 21 * 12 } ) = 100° 24'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 123.93 }{ 29.5 } = 4.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 26° 59'51" } = 13.22 ; ;




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