12 16 26 triangle

Obtuse scalene triangle.

Sides: a = 12   b = 16   c = 26

Area: T = 66.74657863839
Perimeter: p = 54
Semiperimeter: s = 27

Angle ∠ A = α = 18.71769506574° = 18°43'1″ = 0.32766724149 rad
Angle ∠ B = β = 25.33216750167° = 25°19'54″ = 0.44221211341 rad
Angle ∠ C = γ = 135.9511374326° = 135°57'5″ = 2.37327991046 rad

Height: ha = 11.12442977306
Height: hb = 8.3433223298
Height: hc = 5.13442912603

Median: ma = 20.73664413533
Median: mb = 18.60110752377
Median: mc = 5.56877643628

Inradius: r = 2.47220661624
Circumradius: R = 18.6987809519

Vertex coordinates: A[26; 0] B[0; 0] C[10.84661538462; 5.13442912603]
Centroid: CG[12.28220512821; 1.71114304201]
Coordinates of the circumscribed circle: U[13; -13.43990505918]
Coordinates of the inscribed circle: I[11; 2.47220661624]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.2833049343° = 161°16'59″ = 0.32766724149 rad
∠ B' = β' = 154.6688324983° = 154°40'6″ = 0.44221211341 rad
∠ C' = γ' = 44.04986256741° = 44°2'55″ = 2.37327991046 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 = 16 ; ; c = 26 ; ;

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

p = a+b+c = 12+16+26 = 54 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 54 }{ 2 } = 27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27 * (27-12)(27-16)(27-26) } ; ; T = sqrt{ 4455 } = 66.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 66.75 }{ 12 } = 11.12 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 66.75 }{ 16 } = 8.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 66.75 }{ 26 } = 5.13 ; ;

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**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 18° 43'1" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-12**2-26**2 }{ 2 * 12 * 26 } ) = 25° 19'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-12**2-16**2 }{ 2 * 16 * 12 } ) = 135° 57'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 66.75 }{ 27 } = 2.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 12 }{ 2 * sin 18° 43'1" } = 18.7 ; ;




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