18 23 26 triangle

Acute scalene triangle.

Sides: a = 18   b = 23   c = 26

Area: T = 202.2155077331
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 42.55655425086° = 42°33'20″ = 0.74327343317 rad
Angle ∠ B = β = 59.78877229044° = 59°47'16″ = 1.0433492617 rad
Angle ∠ C = γ = 77.6576734587° = 77°39'24″ = 1.35553657049 rad

Height: ha = 22.46883419257
Height: hb = 17.58439197679
Height: hc = 15.55550059485

Median: ma = 22.83663744933
Median: mb = 19.17768089108
Median: mc = 16.04768065359

Inradius: r = 6.03662709651
Circumradius: R = 13.30876130401

Vertex coordinates: A[26; 0] B[0; 0] C[9.05876923077; 15.55550059485]
Centroid: CG[11.68658974359; 5.18550019828]
Coordinates of the circumscribed circle: U[13; 2.84547433673]
Coordinates of the inscribed circle: I[10.5; 6.03662709651]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137.4444457491° = 137°26'40″ = 0.74327343317 rad
∠ B' = β' = 120.2122277096° = 120°12'44″ = 1.0433492617 rad
∠ C' = γ' = 102.3433265413° = 102°20'36″ = 1.35553657049 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 = 18 ; ; b = 23 ; ; c = 26 ; ;

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

p = a+b+c = 18+23+26 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-18)(33.5-23)(33.5-26) } ; ; T = sqrt{ 40890.94 } = 202.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 202.22 }{ 18 } = 22.47 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 202.22 }{ 23 } = 17.58 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 202.22 }{ 26 } = 15.56 ; ;

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{ 18**2-23**2-26**2 }{ 2 * 23 * 26 } ) = 42° 33'20" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23**2-18**2-26**2 }{ 2 * 18 * 26 } ) = 59° 47'16" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-18**2-23**2 }{ 2 * 23 * 18 } ) = 77° 39'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 202.22 }{ 33.5 } = 6.04 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18 }{ 2 * sin 42° 33'20" } = 13.31 ; ;




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