7 26 27 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 26   c = 27

Area: T = 90.99545053286
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 15.02551850802° = 15°1'31″ = 0.26222389504 rad
Angle ∠ B = β = 74.34551782964° = 74°20'43″ = 1.29875681443 rad
Angle ∠ C = γ = 90.63296366234° = 90°37'47″ = 1.5821785559 rad

Height: ha = 25.99884300939
Height: hb = 76.999577333
Height: hc = 6.7440333728

Median: ma = 26.27326093108
Median: mb = 14.83223969742
Median: mc = 13.42657215821

Inradius: r = 3.03331501776
Circumradius: R = 13.50108151928

Vertex coordinates: A[27; 0] B[0; 0] C[1.88988888889; 6.7440333728]
Centroid: CG[9.63296296296; 2.24767779093]
Coordinates of the circumscribed circle: U[13.5; -0.14883606065]
Coordinates of the inscribed circle: I[4; 3.03331501776]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.975481492° = 164°58'29″ = 0.26222389504 rad
∠ B' = β' = 105.6554821704° = 105°39'17″ = 1.29875681443 rad
∠ C' = γ' = 89.37703633766° = 89°22'13″ = 1.5821785559 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 = 7 ; ; b = 26 ; ; c = 27 ; ;

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

p = a+b+c = 7+26+27 = 60 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 60 }{ 2 } = 30 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30 * (30-7)(30-26)(30-27) } ; ; T = sqrt{ 8280 } = 90.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 90.99 }{ 7 } = 26 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 90.99 }{ 26 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 90.99 }{ 27 } = 6.74 ; ;

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{ 7**2-26**2-27**2 }{ 2 * 26 * 27 } ) = 15° 1'31" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-7**2-27**2 }{ 2 * 7 * 27 } ) = 74° 20'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-7**2-26**2 }{ 2 * 26 * 7 } ) = 90° 37'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 90.99 }{ 30 } = 3.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 15° 1'31" } = 13.5 ; ;




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