16 18 26 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 18   c = 26

Area: T = 141.9865914794
Perimeter: p = 60
Semiperimeter: s = 30

Angle ∠ A = α = 37.35768519729° = 37°21'25″ = 0.65220000651 rad
Angle ∠ B = β = 43.04990798002° = 43°2'57″ = 0.75113481825 rad
Angle ∠ C = γ = 99.59440682269° = 99°35'39″ = 1.7388244406 rad

Height: ha = 17.74882393493
Height: hb = 15.77662127549
Height: hc = 10.92219934457

Median: ma = 20.88106130178
Median: mb = 19.62114168703
Median: mc = 11

Inradius: r = 4.73328638265
Circumradius: R = 13.18444063738

Vertex coordinates: A[26; 0] B[0; 0] C[11.69223076923; 10.92219934457]
Centroid: CG[12.56441025641; 3.64106644819]
Coordinates of the circumscribed circle: U[13; -2.19774010623]
Coordinates of the inscribed circle: I[12; 4.73328638265]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.6433148027° = 142°38'35″ = 0.65220000651 rad
∠ B' = β' = 136.95109202° = 136°57'3″ = 0.75113481825 rad
∠ C' = γ' = 80.40659317731° = 80°24'21″ = 1.7388244406 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 = 16 ; ; b = 18 ; ; c = 26 ; ;

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

p = a+b+c = 16+18+26 = 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 * (30-16)(30-18)(30-26) } ; ; T = sqrt{ 20160 } = 141.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 141.99 }{ 16 } = 17.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 141.99 }{ 18 } = 15.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 141.99 }{ 26 } = 10.92 ; ;

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{ 16**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 37° 21'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 43° 2'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-18**2 }{ 2 * 18 * 16 } ) = 99° 35'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 141.99 }{ 30 } = 4.73 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 21'25" } = 13.18 ; ;




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