14 15 26 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 26

Area: T = 83.43222329798
Perimeter: p = 55
Semiperimeter: s = 27.5

Angle ∠ A = α = 25.33216750167° = 25°19'54″ = 0.44221211341 rad
Angle ∠ B = β = 27.28551265654° = 27°17'6″ = 0.47662152954 rad
Angle ∠ C = γ = 127.3833198418° = 127°23' = 2.22332562241 rad

Height: ha = 11.91988904257
Height: hb = 11.12442977306
Height: hc = 6.41878640754

Median: ma = 20.03774649095
Median: mb = 19.48771752699
Median: mc = 6.44220493634

Inradius: r = 3.03438993811
Circumradius: R = 16.36105833291

Vertex coordinates: A[26; 0] B[0; 0] C[12.44223076923; 6.41878640754]
Centroid: CG[12.81441025641; 2.13992880251]
Coordinates of the circumscribed circle: U[13; -9.9333211307]
Coordinates of the inscribed circle: I[12.5; 3.03438993811]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.6688324983° = 154°40'6″ = 0.44221211341 rad
∠ B' = β' = 152.7154873435° = 152°42'54″ = 0.47662152954 rad
∠ C' = γ' = 52.61768015821° = 52°37' = 2.22332562241 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 = 14 ; ; b = 15 ; ; c = 26 ; ;

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

p = a+b+c = 14+15+26 = 55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 55 }{ 2 } = 27.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 27.5 * (27.5-14)(27.5-15)(27.5-26) } ; ; T = sqrt{ 6960.94 } = 83.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.43 }{ 14 } = 11.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.43 }{ 15 } = 11.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.43 }{ 26 } = 6.42 ; ;

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{ 14**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 25° 19'54" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-26**2 }{ 2 * 14 * 26 } ) = 27° 17'6" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 127° 23' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.43 }{ 27.5 } = 3.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 25° 19'54" } = 16.36 ; ;




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