15 18 26 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 18   c = 26

Area: T = 131.213332821
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 34.10770388766° = 34°6'25″ = 0.59552801265 rad
Angle ∠ B = β = 42.2990422069° = 42°17'26″ = 0.73881071072 rad
Angle ∠ C = γ = 103.6032539054° = 103°36'9″ = 1.80882054199 rad

Height: ha = 17.4955110428
Height: hb = 14.579925869
Height: hc = 10.09333329392

Median: ma = 21.06553744329
Median: mb = 19.22223827867
Median: mc = 10.27113192921

Inradius: r = 4.44879094309
Circumradius: R = 13.37551656477

Vertex coordinates: A[26; 0] B[0; 0] C[11.09661538462; 10.09333329392]
Centroid: CG[12.36553846154; 3.36444443131]
Coordinates of the circumscribed circle: U[13; -3.14656408097]
Coordinates of the inscribed circle: I[11.5; 4.44879094309]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.8932961123° = 145°53'35″ = 0.59552801265 rad
∠ B' = β' = 137.7109577931° = 137°42'34″ = 0.73881071072 rad
∠ C' = γ' = 76.39774609457° = 76°23'51″ = 1.80882054199 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 = 15 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 15+18+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 * (29.5-15)(29.5-18)(29.5-26) } ; ; T = sqrt{ 17216.94 } = 131.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.21 }{ 15 } = 17.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.21 }{ 18 } = 14.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.21 }{ 26 } = 10.09 ; ;

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{ 15**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 34° 6'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 42° 17'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-18**2 }{ 2 * 18 * 15 } ) = 103° 36'9" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.21 }{ 29.5 } = 4.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 34° 6'25" } = 13.38 ; ;




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